It's easy to be an ideologue on the internet. IRL people vote with actions and it's why even in places like SF, LA and NYC we see so many people send their kids to private schools - even religious ones.
I'll share my experience. I went to Catholic School. It was:
1) extremely diverse - racially, ethnically and economically
2) we had Jewish, Muslim and atheist kids who attended
3) it was very progressive (in fact my school is one of only 60 in the country to have AP African American history)
Why did such a diverse group attend a Catholic school? It's both an excellent school and because many didn't want to attend Oakland public schools.
So people are free to say they don't like religion. But non Catholic private schools usually cost about double the amount. For some, writing that $50K/yr check for their kid's education is nothing. But for many it's not an easy task, hence the appeal of Catholic schools.