On what grounds does the Catholic church reject sacraments of protestant denominations?

I think there are two reasons protestants may tend to be more relaxed about this than Catholics.

The first comes down to the word "Sacrament". Many, perhaps even most, protestants just don't believe in sacraments as such. Sure, we believe there are things we are commanded to do as part of our worship, but instead of rising to the level of a sacrament we would instead say that a Christian who fails to do such things sins, and praise God for the grace made possible by the blood of Jesus. So because of the idea that the sacraments are less directly connected to salvation and membership in the body of Christ, it makes less sense to be strict about rules of who, when, and where.

The second is that protestants have a more direct line to God, so to speak. We don't seek approval of any priest, bishop, cardinal, or pope, and therefore don't need their permission to participate in any act of worship. Neither would we want to deny that worship to anyone else, but instead want to make the Good News accessible to as many as possible as easily as possible.

Regarding the scriptural authority for the central church, Christ gave us the church first not the new testament. He celebrated two masses before ascending to heaven. One the last supper and the second on the road to Emmaus. The new testament was written much later than the ascension and the compilation of the new testament complete with translations did not occur until around the 4th century through the work of a Catholic Priest, now known as St Jerome. So the Holy Church is the mother of the Bible not the other way around. God speaks to us through the Bible. He provided the apostles the ability to forgive or retain sin, Consecrate the Eucharist and grow His Holy Church through baptism and preaching. Saint Paul was clear about adhering to both the written and oral traditions we have been taught. The Catholic Church also considers Christians with belief in the Trinity to be members of the Catholic church and we are all God willing headed to the same place! For questions on the Eucharist, I recently saw an excellent video entitled Science Tests Faith. I love my fellow Christians but I will confess I am saddened that the belief in the body of Christ has been somewhat lost along the way. He did say "This is my body" Watch the video and give it some thought. God bless everyone.

I'm not sure, but I don't think that it's required to get re-married if a couple converts to Catholicism. While researching an answer to this question on annulment, I found multiple sources that say:

...every marriage, whether between Catholics, Christians of other denominations, or non-baptized persons, is presumed to be valid.

The Roman Catholic Church recognizes not only Protestant Church marriages but also sees those marriages as sacramental in nature (Just like Catholic marriages) provided both Husband and Wife are baptized. The Roman Catholic Church however, looks upon non-Christian marriages as valid (for instance a Jewish, Muslim or Indian marriage). But, in the eyes of the Church, they are "Natural", that is non-sacramental marriages.

A word of caution, unlike the Orthodox Church, the Catholic Church takes a literal view of marriage based upon the Gospel of Saint Matthew Chapter 19. Additionally, Christ began His Ministry at a wedding festival (Cana), and ended his human life on the Cross. The Church has always viewed the Church as the Bride of Christ. And Christ being the perfect spouse, always remains faithful. It is the Church's belief that whenever a Man and Woman come together as Husband and Wife they enter a mystical union (whether they "feel" it or not) that mirrors Christ's love for His Church. The Gospel of Saint Matthew reflects this theological reality. To the Church marriages and the Cross are intimately linked. Ergo, in past eras the Church rarely gave of Statements of Nullity (annulments) for marriages. Furthermore, the Church calls marriages, the Sacrament of Holy Matrimony (or the making of mothers).

If a Protestant Couple converts to Catholicism they do not have to get remarried. They could have their marriage blessed by a priest just to have an official record of their marriage entered in the local parish and diocese. But, if a Protestant divorces and then converts to Catholicism and later wishes to marry another Catholic, the Protestant will have to go to the diocese's Marriage Tribunal and petition to have their previous marriage annulled. This is where much contention begins. The average time frame for an annulment is 2-3 years. And there is no guarantee that the Tribunal will approve it. I'm no canon lawyer, so I don't know what kind of circumstances the Tribunal looks at other than things like baptism, an understanding what marriage is, the willingness to have children, etc...

The Church may seem to many people to be hard-hearted and filled with too many rules - especially concerning marriage. But, it takes the long view. It also follows what Christ preached (and in marriage Christ was even harder than Moses). Currently, there is a block of Catholic theologians and clerics who wish to change this. The Synod of the Family will address this issue once again. But, I don't expect any doctrinal changes.

Remarriage is not necessary. The Catholic Church recognizes a Christian marriage as sacramental and indissoluble unless there was something that made it invalid. Catholic communion is radically different from Protestant communion since it is the actual body of Christ. Protestants only believe communion is symbolic. Also, Protestant communion is not the body of Christ because only a Catholic priest can consecrate bread to change it to the body of Christ. Protest pastors lack this power because they did not receive it through apostolic succession. Some orthodox religions that broke off the Catholic Church still have valid masses because the priests the apostolic succession was unbroken. A Protestant cannot receive Catholic Communion until they are instructed in the faith and understand it is the actual body of Christ. Once Catholic then they are initiated into this sacrament as other Catholics at their First Holy Communion.

The question is overly broad and needs to be taken sacrament by sacrament. The question asked specifically about three sacraments: baptism, eucharist, and marriage.

The Catholic Church recognizes any baptism performed according to the church's teachings on baptism, no matter who performs it. From the Catechism of the Catholic Church:

V. WHO CAN BAPTIZE?

1256 The ordinary ministers of Baptism are the bishop and priest and, in the Latin Church, also the deacon.57 In case of necessity, anyone, even a non-baptized person, with the required intention, can baptize58 , by using the Trinitarian baptismal formula. The intention required is to will to do what the Church does when she baptizes. The Church finds the reason for this possibility in the universal saving will of God and the necessity of Baptism for salvation.59

What makes a baptism invalid is 1) using something other than water to baptize, 2) using the wrong words (the baptism must use a trinitarian formula--be in the name of the Father, the Son and the Holy Spirit or Holy Ghost) and 3) intending to do anything other than a Christian baptism (for example, acting out a baptism as part of a theatrical production). If a non-Trinitarian person such as a Mormon attempts to perform a Christian baptism, it will be considered invalid or questionable because then they bring into doubt that they are intending to do as the church does.

In the case of the Eucharist, only a priest is empowered to enact the sacrament acting in the person of Christ the head (in persona Christi capitis) by virtue of his ordination. From the Catechism of the Catholic Church:

1369 The whole Church is united with the offering and intercession of Christ. Since he has the ministry of Peter in the Church, the Pope is associated with every celebration of the Eucharist, wherein he is named as the sign and servant of the unity of the universal Church. The bishop of the place is always responsible for the Eucharist, even when a priest presides; the bishop's name is mentioned to signify his presidency over the particular Church, in the midst of his presbyterium and with the assistance of deacons. The community intercedes also for all ministers who, for it and with it, offer the Eucharistic sacrifice:

• Let only that Eucharist be regarded as legitimate, which is celebrated under [the presidency of] the bishop or him to whom he has entrusted it.191

• Through the ministry of priests the spiritual sacrifice of the faithful is completed in union with the sacrifice of Christ the only Mediator, which in the Eucharist is offered through the priests' hands in the name of the whole Church in an unbloody and sacramental manner until the Lord himself comes.192

Also:

1410 It is Christ himself, the eternal high priest of the New Covenant who, acting through the ministry of the priests, offers the Eucharistic sacrifice. And it is the same Christ, really present under the species of bread and wine, who is the offering of the Eucharistic sacrifice.

1411 Only validly ordained priests can preside at the Eucharist and consecrate the bread and the wine so that they become the Body and Blood of the Lord.

The church also makes a distinction between valid sacraments (those conducted by persons with the power to do so, and according to the prescribed rites of the church) and licit sacraments (those valid sacraments which are legally permitted). At times the church will restrict the right of an ordained priest to conduct the sacraments for disciplinary reasons such as an interdict. At such times, if a sacrament is illicitly performed it is still recognized as valid. In other words, the pope disapproves for whatever reason, but God still provides the grace anyway. Anglicans and Orthodox have preserved an ordained apostolic priesthood but not communion with Rome, so in the absence of other impediments their eucharist is considered valid.

Eucharist also has implications on who can validly receive the sacrament since reception implies a certain level of unity of theology with the local bishop, and indirectly with the pope.

From the Catechism of the Catholic Church:

1399 The Eastern churches that are not in full communion with the Catholic Church celebrate the Eucharist with great love. "These Churches, although separated from us, yet possess true sacraments, above all - by apostolic succession - the priesthood and the Eucharist, whereby they are still joined to us in closest intimacy." A certain communion in sacris, and so in the Eucharist, "given suitable circumstances and the approval of Church authority, is not merely possible but is encouraged."238

1400 Ecclesial communities derived from the Reformation and separated from the Catholic Church, "have not preserved the proper reality of the Eucharistic mystery in its fullness, especially because of the absence of the sacrament of Holy Orders."239 It is for this reason that, for the Catholic Church, Eucharistic intercommunion with these communities is not possible. However these ecclesial communities, "when they commemorate the Lord's death and resurrection in the Holy Supper . . . profess that it signifies life in communion with Christ and await his coming in glory."240

1401 When, in the Ordinary's judgment, a grave necessity arises, Catholic ministers may give the sacraments of Eucharist, Penance, and Anointing of the Sick to other Christians not in full communion with the Catholic Church, who ask for them of their own will, provided they give evidence of holding the Catholic faith regarding these sacraments and possess the required dispositions.241

Marriages are generally valid no matter who officiates because in Catholic theology it is the husband and wife that administer the sacrament to each other. From the Catechism of the Catholic Church:

1623 According to Latin tradition, the spouses as ministers of Christ's grace mutually confer upon each other the sacrament of Matrimony by expressing their consent before the Church. In the tradition of the Eastern Churches, the priests (bishops or presbyters) are witnesses to the mutual consent given by the spouses,124 but for the validity of the sacrament their blessing is also necessary.125

I think @DavidStratton's answer takes a good "root cause" approach but I'd like to look at the surface of things a bit as well. I noted in my comment above that protestant baptisms and marriages are not categorically rejected by the Catholic Church so I'll just focus on communion. There are three main reasons why Catholics wouldn't receive communion from protestants:

• Intercommunion signifies a unity of faith that doesn't exist. For Catholics the act of receiving Holy Communion is, among many other things, a public statement of faith: "I believe what this Church teaches in general, and I believe in particular what this Church teaches about the Eucharist"

• Most protestants don't believe the doctrine that in Catholic traditional language is called "transubstantiation". So in a Catholic's eyes, a protestant community holding a communion service is, objectively speaking, doing something other than what the Lord commanded in Luke 22:19. This obviously makes for some insurmountable difficulties.

• Even those protestants who do believe in transubstantiation, by whatever name, almost certainly don't believe in an ordained priesthood in the same way that Catholics do -- which would almost certainly mean that they don't have what the Catholic Church would consider a valid priesthood. And only validly ordained priests are able to confect the Eucharist validly. So even in the (I assume rare?) case of a protestant community that professes a faith in the Eucharist which is indistinguishable from the Catholic doctrine, there would still be the objective problem of validity of the sacrament.