As to the OP, as one who has been in all three camps (RCC, evangelical, and Orthodoxy), it is something I have thought about.
I try to see the side of the others . . . and usually succeed.
To the Bible-believing Protestant, he sincerely is trying to save others from error.
To the RCC (and especially here many converts to that church), they see God's work in a more expanded way through the church and it's reality.
For the Orthodox, we claim that the Holy Spirit is in the Orthodox Church, but he blows where ever He wills.
While as someone posted, one can be sincere but sincerely wrong, that is true, but we see even Paul's view evolve in the New Testament.
Sincerity is enough to have a good relationship with my brother (or sister) of a different faith tradition.
Now, you can say Nazis were sincere in their beliefs, which is true. But there beliefs are not based in
love or in the true God. What we have in common is we worship the same God of love. And that is
enough to find common ground.