"Present almost everywhere" is in fact what pervasive means :)
The thesaurus lists these words as some synonyms of pervasive:
Widespread, prevalent, common, present, popular, majority, predominant.[0]
Just because the culture isn't accepted by every single person on planet earth doesn't mean it's not pervasive. There were plenty of pockets of communities in the early 20th century and late 19th century that didn't follow the traditional norms of Christianity that existed in the west. But I think we would both agree that Christianity/catholicism was pervasive in the west in those time periods.
After all, Nietzsche, Oscar Wilde, Darwin, Marx, Bertrand Russell and more were popular with different communities at the time, even though they were definitely counter to the pervasive culture of Christianity/catholicism then.
And I agree with you about how it's surprising that even at a Christian university, the traditional values of Christianity aren't taught! The example I gave was just one of the things I thought of off the top of my head. There were several other examples that gave me the feeling that the majority of the students weren't interested in traditional values. Chapel was a running joke among the students, nobody really cared and just went since the credit was required. People in positions of leadership that didn't align with the trendy culture slowly got replaced throughout my time there. We routinely got lectured on diversity and equity and how the university was devoted to it. I have friends who are gay that let me know how widespread the lgbt+ community at the university was (among professors and students).
I could go on, but my point was that even in the rural south, plenty of people are afraid to go against the trendy culture. My experience was simply some anecdata to your presumption that the rural South does not have a significant majority of people also following the trends of liberal cities. It's definitely less pronounced, but it's also definitely pervasive.
