The California Church of Christ must be more "liberal" than the Texas brand. I have two great uncles who are Church of Christ ministers and they firmly believe my mother is NOT going to Heaven because she joined the Catholic church. They don't say she's going to Hell, they just say she is not going to Heaven (if that makes any difference).
My point is that there are many evangelicals and other "Bible Belt" Christians who make very clear boundaries between what denominations they will accept and what they will not. And sometimes they even draw lines within their own denomination. The local Church of Christ where I live had a huge falling out a few years ago when they built a new church. Most of the people wanted to have a kitchen in the new building, but a small faction of old timers (lead by my mother's first cousin who is also a Church of Christ minister) said it was against the Bible to have a kitchen in the church building.
I've heard that before, and I have trouble believeing it. Do the loudest people in these churches have beliefs like this? Perhaps. But I'd like to think that at least a majority of them actually read the Bible and know what they are talking about, and there is simply 0 Biblical support for saying all Catholics are barred from heaven.
I could be wrong, but we'll see.