According to the Catholic Church, are Jews saved without faith in Jesus?

What is God's wish for all men?

God desires all men to be saved and to come to the knowledge of the truth.

What does the Church teach about herself and Christ as regards to men's salvation?

The Church teaches "Outside the Church there is no salvation" which re-formulated positively, means that all salvation comes from Christ the Head through the Church which is his Body. [cf. CCC 846].

Therefore whoever will be saved, their salvation in the end would have been from Christ the Head through the Church which is his Body.

Where does faith [in God and in his Christ] feature in men's salvation?

In a couple of numbers below CCC 846, CCC 848 tells us that there is a faith [in God and in his Christ] without which it is impossible to please [God].

Therefore, no one, Catholic or non-Catholic, Christian or non-Christian, Jew or Gentile can be saved without Christ, faith in him and through his body the Church.

Has God rejected the Jews because they have not [yet] accepted the Gospel?

Not so fast. St. Paul in scripture tells us that there is a mystery here, and God precisely used this rejection to bring gentiles to him:

Israel’s Rejection Is Not Final
11 I ask, then, has God rejected his people? By no means! I myself am an Israelite, a descendant of Abraham, a member of the tribe of Benjamin. 2 God has not rejected his people whom he foreknew.

[...]

All Israel Will Be Saved
25 Lest you be wise in your own conceits, I want you to understand this mystery, brethren: a hardening has come upon part of Israel, until the full number of the Gentiles come in, 26 and so all Israel will be saved; as it is written,

“The Deliverer will come from Zion, he will banish ungodliness from Jacob”; 27 “and this will be my covenant with them when I take away their sins.”

28 As regards the gospel they are enemies of God, for your sake; but as regards election they are beloved for the sake of their forefathers. 29 For the gifts and the call of God are irrevocable. 30 Just as you were once disobedient to God but now have received mercy because of their disobedience, 31 so they have now been disobedient in order that by the mercy shown to you they also may[b] receive mercy. 32 For God has consigned all men to disobedience, that he may have mercy upon all.

[...]

Cf. Romans 11 (RSVCE)

The Vatican under the pontificate of Pope Francis and even Pope Francis himself have not been precise in language resulting in confusion and consternation of the faithful and others. Catholics know their faith and what is the perennial teaching of the Church, the faithful spouse of Christ.

Cf.
- POPE: Don't Evangelize Jews! Really?, by Jimmy Akin | NCR.
- New Vatican Document on Jews, Salvation, and Evangelization, by Jimmy Akin | NCR.

If that document indeed says Jews can be saved without the Catholic Faith, it is contrary to dogmatic teaching expressed, e.g., in the Council of Florence's decree Cantate Domino (Denz. 714), ratified by Pope Eugene IV:

The sacrosanct Roman 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.

One is "added to the flock" (i.e., made a member of the Catholic Church) by professing the Catholic Faith and being baptized, as Pope Pius XII wrote in Mystici Corporis Christi §22:

Actually only those are to be included as members of the Church who have been baptized and profess the true faith, and who have not been so unfortunate as to separate themselves from the unity of the Body, or been excluded by legitimate authority for grave faults committed. "For in one spirit" says the Apostle, "were we all baptized into one Body, whether Jews or Gentiles, whether bond or free."[I Cor., XII, 13.] …

Thus, Jews (and anyone else, too) must be baptized and profess the Catholic Faith to be saved.

^{(cf. John 8:19, where Jesus says to the Pharisees, the precursors of modern-day Talmudic Jews: “You know neither me nor my Father. If you knew me, you would know my Father also.”)}

See

• this in-depth analysis of the heterodoxy of the Vatican's recent document

and

• pp. 31-41 of famous 20th century Catholic theologian Msgr. Fenton's The Catholic Church and Salvation.

Paragraphs 35 and 36 of the document discussed by the news article you've linked to state (emphasis mine):

35. Since God has never revoked his covenant with his people Israel, there cannot be different paths or approaches to God’s salvation. The theory that there may be two different paths to salvation, the Jewish path without Christ and the path with the Christ, whom Christians believe is Jesus of Nazareth, would in fact endanger the foundations of Christian faith. Confessing the universal and therefore also exclusive mediation of salvation through Jesus Christ belongs to the core of Christian faith. So too does the confession of the one God, the God of Israel, who through his revelation in Jesus Christ has become totally manifest as the God of all peoples, insofar as in him the promise has been fulfilled that all peoples will pray to the God of Israel as the one God (cf. Is 56:1-8). The document "Notes on the correct way to present the Jews and Judaism in preaching and catechesis in the Roman Catholic Church" published by the Holy See’s Commission for Religious Relations with the Jews in 1985 therefore maintained that the Church and Judaism cannot be represented as "two parallel ways to salvation", but that the Church must "witness to Christ as the Redeemer for all" (No.I, 7). The Christian faith confesses that God wants to lead all people to salvation, that Jesus Christ is the universal mediator of salvation, and that there is no "other name under heaven given to the human race by which we are to be saved" (Acts 4:12).

36. From the Christian confession that there can be only one path to salvation, however, it does not in any way follow that the Jews are excluded from God’s salvation because they do not believe in Jesus Christ as the Messiah of Israel and the Son of God. Such a claim would find no support in the soteriological understanding of Saint Paul, who in the Letter to the Romans not only gives expression to his conviction that there can be no breach in the history of salvation, but that salvation comes from the Jews (cf. also Jn 4:22). God entrusted Israel with a unique mission, and He does not bring his mysterious plan of salvation for all peoples (cf. 1 Tim 2:4) to fulfillment without drawing into it his "first-born son" (Ex 4:22). From this it is self-evident that Paul in the Letter to the Romans definitively negates the question he himself has posed, whether God has repudiated his own people. Just as decisively he asserts: "For the gifts and the call of God are irrevocable" (Rom 11:29). That the Jews are participants in God’s salvation is theologically unquestionable, but how that can be possible without confessing Christ explicitly, is and remains an unfathomable divine mystery. It is therefore no accident that Paul’s soteriological reflections in Romans 9-11 on the irrevocable redemption of Israel against the background of the Christ-mystery culminate in a magnificent doxology: "Oh, the depth of the riches and wisdom and knowledge of God! How inscrutable are his judgments and how unsearchable his ways" (Rom 11:33). Bernard of Clairvaux (De cons. III/I,3) says that for the Jews "a determined point in time has been fixed which cannot be anticipated".

In summary, it appears that the document reiterates previously published Catholic documents that while the Jews are saved through Christ, their "participation" in the salvation of God is not a result of faith in Christ Jesus as Messiah but rather of the promises that God has made to them, which are irrevocable. Since this is contrary to the traditional understanding of salvation through faith and confession in Jesus Messiah, the document refers to the salvation of the Jews through Christ as a mystery. We continue to read in paragraph 37:

Here we confront the mystery of God’s work, which is not a matter of missionary efforts to convert Jews, but rather the expectation that the Lord will bring about the hour when we will all be united, "when all peoples will call on God with one voice and ‘serve him shoulder to shoulder’.

The document does reiterate the Vatican II position on organized mission work directed toward Jews in paragraph 40:

It is easy to understand that the so–called ‘mission to the Jews’ is a very delicate and sensitive matter for Jews because, in their eyes, it involves the very existence of the Jewish people. This question also proves to be awkward for Christians, because for them the universal salvific significance of Jesus Christ and consequently the universal mission of the Church are of fundamental importance. The Church is therefore obliged to view evangelisation to Jews, who believe in the one God, in a different manner from that to people of other religions and world views. In concrete terms this means that the Catholic Church neither conducts nor supports any specific institutional mission work directed towards Jews.

For a thorough exposition of the Roman Catholic doctrines concerning salvation, please read the article on that topic at CARM.

As for the history of relations between Catholicism and Judaism and the Roman Catholic Church's teachings, please read the Wikipedia article on that subject as a touchstone. It appears that the Catholic Church's teachings on the subject have been constant over the ages, and that Vatican II (1962 - 1965) was a turning point in the Vatican's position on the salvation of the Jews, as it was on many other doctrines. Specifically, the document titled Nostra Aetate deals with doctrines concerning the Jewish people. The Wikipedia article, which offers a brief historical background and a few modern considerations, states:

A new understanding of the relationship between Catholics and Jews is also reflected in the revised liturgy of Good Friday in a particular way. The pre-1962 version of the Good Friday Prayer of the Roman Rite had Catholics praying that the "perfidis Judaeis" might be converted to "the truth." The English cognate "perfidious" had, over the centuries, gradually acquired the sense of "treacherous." In order to eliminate misunderstanding on this point, Pope Pius XII ordered in 1955 that, in Catholic liturgical books, the Latin word "perfidis" be properly translated "unbelieving", ensuring that the prayer be understood in its original sense: praying for the Jews who remained "unbelieving" concerning the Messiah. Indeed, the same adjective was used in many of the ancient rituals for receiving non-Christian converts into the Catholic Church.

Here are excerpts from the two Good Friday prayers, before Vatican II,

Let us pray likewise for the unbelieving Jews: that the Lord our God may remove from their hearts the veil of unbelief: and that they may come to the knowledge of Jesus Christ our Lord.

...and after:

Let us pray
For the Jewish people,
The first to hear the word of God,
That they may continue to grow in the love of his name
And in faithfulness to his covenant.

The document under discussion is no new thing, but is meant to be a reflection upon Nostra Aetate on the fiftieth anniversary of its publication. Historically, the change in doctrine toward the salvation of the Jews represented by that document appears to be a recent and legitimate about-face from Tradition, since Church Fathers, Magisterial congregations, and Popes as recent as the twentieth century, have made clear statements that while the Jews should be especially protected from persecution, they can not be justified by their ancestry alone but only by conversion to the Universal Faith.

Again from Wikipedia,

Around 598, in reaction to anti-Jewish attacks by Christians in Palermo, Pope Gregory the Great (c 540–604) brought Augustine's teachings into Roman Law, by writing a Papal Bull which became the foundation of Catholic doctrine in relation to the Jews and specified that, although the Jews had not accepted salvation through Christ, and were therefore condemned by God until such time as they accept salvation, Christians were nevertheless duty-bound to protect the Jews as an important part of Christian civilization. The Bull said that Jews should be treated equitably and justly, that their property rights should be protected, and that they should keep their own festivals and religious practices. Thus, in the Papal States, Jews enjoyed a level of protection in law.