>>550699
>Is Extra Ecclesiam nulla salus' dogmatic catholic belief?
yes
>Are catholics required to believe that christians from other denominations are doomed to hell?
no one is "doomed to hell" strictly speaking, only God knows that, but if you're saved while being outside of the Catholic Church, it'll be in spite of, and not because of, what you believe.
furthermore, if you actively reject Catholic doctrine, you're rejecting the truth and essentially calling good "evil," so you're certainly not putting the odds of salvation on your side.
the Orthodox believe the same thing, since we believe we are the Catholic Church. however, while Roman Catholics agree that there can be sacraments outside of the Church (and so, all validly baptized people are in imperfect communion with the Church, and this communion is even closer to perfection for those who have valid sacraments like the Eucharist), there is no such consensus in the Orthodox Church.