It's kind of amusing though, because while creating "safe" schools for largely white people, many of these same churches also geared up to accept daycare vouchers from the government and had a decidedly different demographic in the kindergarten than the grade school.
I often find common perceptions about Catholic schools to be amusing but ignorant. In many places, the Catholic schools were staffed by nuns and priests who live communally and had/have some pretty liberal politics. My elementary school was just such a place. Our student body was actually more diverse than the public school by standard measures, and had a special relationship with the synagogue down the street because it was the only private school where the Jews (maybe two dozen families in the entire town) would send their kids. Our youth priest was a hippie and the Monsignor was a social mover and shaker in our rural area where Catholics were a minority.