Why do Catholics teach that Catholics go to hell if they die in a state of mortal sin, but teach some Protestants may go to Purgatory/Heaven?

It is solemnly-defined dogma—defined, e.g., in Pope Eugene IV's Cantate Domino (1442)—that the Catholic Church

firmly believes, professes, and proclaims that those not living within the Catholic Church, not only pagans, but also Jews and heretics and schismatics cannot become participants in eternal life, but will depart “into everlasting fire which was prepared for the devil and his angels” [Matt. 25:41], unless before the end of life the same have been added to the flock; and that the unity of the ecclesiastical body is so strong that only to those remaining in it are the sacraments of the Church of benefit for salvation, and do fastings, almsgiving, and other functions of piety and exercises of Christian service produce eternal reward, and that no one, whatever almsgiving he has practiced, even if he has shed blood for the name of Christ, can be saved, unless he has remained in the bosom and unity of the Catholic Church.

Protestants are heretics and schismatics for several reasons, such as not believing in the

1. Papacy

   Pope Boniface VIII, Unam Sanctam, 1302:
   

   Furthermore, we declare, we proclaim, we define that it is absolutely necessary for salvation that every human creature be subject to the Roman Pontiff.

2. transubstantiation

   13th session of the Council of Trent (October 11, 1551):
   

   Canon I.—If any one denieth, that, in the sacrament of the most holy Eucharist, are contained truly, really, and substantially, the body and blood together with the soul and divinity of our Lord Jesus Christ, and consequently the whole Christ; but saith that he is only therein as in a sign, or in figure, or virtue: let him be anathema.

3. sacrificial nature of Holy Mass

   22nd session of the Council of Trent (September 17, 1562):
   

   Canon I.—If any one saith, that in the mass a true and proper sacrifice is not offered to God; or, that to be offered is nothing else but that Christ is given us to eat: let him be anathema.

4. ministerial priesthood and visibility of the Church

   23rd session of the Council of Trent (July 15, 1563):
   

   Canon I.—If any one saith, that there is not in the New Testament a visible and external priesthood; or, that there is not any power of consecrating and offering the true body and blood of the Lord, and of forgiving and retaining sins, but only an office and bare ministry of preaching the Gospel; or, that those who do not preach are not priests at all: let him be anathema.

5. purgatory, invocation, veneration, and relics of saints, and sacred images

   25th and final session of the Council of Trent (December 4, 1563):
   

   But if any one shall teach or entertain sentiments contrary to these decrees: let him be anathema.

Bl. Pope Pius IX condemned the following proposition in his Syllabus of Errors (December 8, 1864):

18. Protestantism is nothing else than a different form of the same true Christian religion, in which it is possible to serve God as well as in the Catholic Church

Therefore, since salvation requires "remain[ing] in the bosom ^{[i.e., being subject to the Roman Pontiff]} and unity ^{[i.e., professing the Catholic faith, whole and entire, which alone binds members of the Mystical Body of Christ together]} of the Catholic Church," Protestants cannot be saved unless they convert and profess the one, true, Catholic Faith.

Some Protestants, such as those brought up in non-Catholic surroundings and who have not heard Catholic teaching, act in good faith (bona fide) and are ignorant of their sins against the faith. They are material heretics. Consequently, they have no guilt or sin against the faith. Their salvation, however, is not guaranteed. If they are saved, their salvation is through the Catholic Church, not their heretical sect.

^{cf. the resources here on extra Ecclesiam [Catholicam] nulla salus ("outside the [Catholic] Church there is no salvation")}

The following, represents the Roman Catholic Church, not the context of a document taken out of time condemning active heretics, those who rebelled as Satan did, but those who fell victim to that rebellion.

The affirmation "outside the Church there is no salvation" is explained in the Catechism of the Catholic Church (§846-848) as follows:

How are we to understand this affirmation, often repeated by the Church Fathers? Re-formulated positively, it means that all salvation comes from Christ the Head through the Church which is his Body: Basing itself on Scripture and Tradition, the Council teaches that the Church, a pilgrim now on earth, is necessary for salvation: the one Christ is the mediator and the way of salvation; he is present to us in his Body which is the Church. He himself explicitly asserted the necessity of faith and baptism, and thereby affirmed at the same time the necessity of the Church which men enter through baptism as through a door. Hence they could not be saved who, knowing that the Catholic Church was founded as necessary by God through Christ, would refuse either to enter it or to remain in it.

This affirmation is not aimed at those who, through no fault of their own, do not know Christ and his Church: Those who, through no fault of their own, do not know the Gospel of Christ or his Church, but who nevertheless seek God with a sincere heart, and, moved by grace, try in their actions to do his will as they know it through the dictates of their conscience—those too may achieve eternal salvation.

Although in ways known to himself God can lead those who, through no fault of their own, are ignorant of the Gospel, to that faith without which it is impossible to please him, the Church still has the obligation and also the sacred right to evangelize all men.

This situation, although possible, is not nor should it be even remotely considered likely Only possible.

^{Much of this answer was borrowed from Catholic Answers at Catholic.com.}