General Catholic Approach to Religions of the World
The basis of the Catholic approach to the religions of the world is found in the document Nostra Aetate. First of all, in order to understand the Catholic approach, one must first understand why having this refined approach is important: the world is becoming more interconnected with technological advancements and encounters between people of various religions are becoming even more commonplace. For this reason, it's vital that Catholics foster unity and love between all people of all religions. Therefore, the Catholic approach is meant to foster this unity and love by not condemning other religions, but rather stressing the commonalities between them. Nostra Aetate states that "the Catholic Church rejects nothing of what is true and holy" in the religions of the world, meaning that objective truth (which is also inherently Catholic truth) can be found in religions other than Catholicism, and as Catholics, we must seek that truth.
Approach to Hinduism, Buddhism, Islam, and Judaism
Nostra Aetate emphasizes the commonalities of religions around the world to Catholicism in order to foster unity between them:
Hinduism stresses a searching of divine mystery in similar ways to Catholicism. They also seek a freedom from the human condition just as Catholics.
Similarly, Buddhists realize the insufficiency of our world and attempt to reach a transcendent state of perfection, which is much like the Catholic journey to Heaven.
Islam holds the same God as Catholics to be the one and true God and share origins with Catholics such as Abraham.
Judaism also holds the same God as Catholics to be true and share origins with the Catholic Church. In addition, Jesus himself was Jewish and much of our Old Testament comes from Jewish scripture.
Furthermore, the Catholic approach stresses that even though there are differences between the religions of the world and Catholicism, the Catholic Church still very much respects the religions of the world. Nostra Aetate speaks about respecting the religions of the world, specifically Islam and Judaism. Both Muslims and Jews believe in the same God as Catholics, yet they have been meet with much animosity throughout history, however, this is not the Catholic way. As Catholics, we ought to embrace people of other religions and approach them with love. The document also speaks specifically about Jews in saying that they can not be blamed for the death of Jesus, which was a point of tension between Catholics and Jews. It articulates that the Catholic approach is not to condemn the Jewish people because they are not to blame, but rather to show them love and respect.
What does this mean on a smaller, individual scale? It means that as Catholics, when we encounter someone of another faith, we should not stress differences and should not condemn them for not being Catholic, rather, we ought to show those individuals love and respect. We should not be confrontational, but approach and treat them in a way that Jesus would've. That is the Catholic approach to world religions: love and respect.
What does this mean for the salvation of participants of non-Christian religions?
Obviously I cannot determine whether people will achieve salvation or not; that is completely up to God; however, it is important to have an understanding of ignorance as it pertains to salvation. There are two types of ignorance: invincible and vincible. Invincible ignorance means that the individual has not been exposed to Jesus and Christianity and had no opportunity to encounter it and vincible ignorance means that the person did have an opportunity to encounter Christianity but chose to not pursue it, to ignore it, or to not seek further information about it. Based on our understanding of God, it's reasonable to infer that he would not simply condemn someone who was invincibly ignorant of him if they live a good and Christ-like life. In addition, we cannot determine if someone who lives a Christ-like life, yet practices another religion and is vincibly ignorant of Christianity can achieve salvation, it is all up to God and his judgement. But, we do know that God works in mysterious ways and is not limited to the Catholic Church. In addition, the Catholic Church has not made any definitive statements on this issue, however, we do know that the Church is meant to bring salvation to its members and is the dwelling place of God. Therefore, salvation through other religions is for the most part a mystery to us.