Question:  Catholics believe that salvation is possible for everyone whatever their religion. Good people who are not members of the Catholic Church, such as Jews and Muslims, can be saved also.

Answer: Your statement reflects the teaching of the Catholic Church after the second Vatican council. However this was not always what Rome taught. Please read carefully the following quotations:

"There is but one universal Church of the faithful, outside of which no one at all can be saved" (Pope Innocent III, Fourth Lateran Council).

"We declare, say, define, and pronounce that it is absolutely necessary for the salvation of every human creature to be subject to the Roman Pontiff" (Pope Boniface VIII, Unam Sanctam).

"The most Holy Roman Church firmly believes, professes, and preaches that none of those existing outside the Catholic Church, not only pagans, but also Jews and heretics and schismatics, can have a share in life eternal; but that they will go into the eternal fire which was prepared for the devil and his angels, unless before death they are joined with Her; and that so important is the unity of this ecclesiastical body that only those remaining within this unity can profit by the sacraments of the Church unto salvation, and they alone can receive an eternal recompense for their fasts, their almsgiving, their other works of Christian piety and the duties of a Christian soldier. No one, let his almsgiving be as great as it may, no one, even if he pour out his blood for the Name of Christ, can be saved, unless he remain within the bosom and the unity of the Catholic Church" (Pope Eugene IV, Cantate Domino).

According to the teaching of the Catholic church, there is no salvation outside the Catholic Church. The reason given by the Pope is that all their good works are useless unless one remains within the bosom and unity of the Church.

The position taken by the Catholic church historically and that taken after Vatican II are irreconcilable and contradictory. You will find it impossible to admit that the Church was mistaken; with such an acknowledgement the whole structure of infallibility falls like a house of cards. But I think that deep down you can feel the tension.