You are correct that some Protestant, or more likely, non-denom, churches, imply that Catholics are essentially lost souls in need of salvation. Given that there are a multitude of core beliefs that we share, I never felt comfortable with that.
It reminds me of the Northern Ireland situation. My in-laws participated in a group that brought one Irish Protestant and one Irish Catholic child to stay with them for a while. The idea I believe was for them to see that they have much more in common than they have differences. I suspect if you put any Christian denoms together in a cleric-ruled Muslim country, they would all quickly band together and forget their differences.