Don't jump to conclusions or post stuff that you did not actually read.
http://ciep.hunter.cuny.edu/catholicschools
"Finally, one of the most important things the authors omitted was a subgroup analysis, to determine how the results might have differed for racial/ethnic and income groups. This would have been helpful, because other research (Figlio & Stone, 1997) has shown that even if results indicate no Catholic school advantage for the general population, minority students, particularly from urban areas, still might benefit substantially. This, in fact, is one of the strongest reasons to promote access to Catholic schools: to narrow the racial and socioeconomic achievement gap. Propensity score matching could handily investigate whether Catholic schools really do benefit racial and ethnic minority students from urban areas."
I love that they really worked hard on the research, but this is a dealbreaker for me.
2nd, I would add that they did not correlate at all dollars spent on education. For all of the complaints about public schools, some of which are legitimate, religious schools do more with less and for less, meaning they get level or superior results at a reduced cost, and (seemingly) achieve better life outcomes, maybe due to religious or character instruction.
https://www.brookings.edu/research/public-or-private-school-it-shouldnt-matter
It's Ravitch. I'm not saying don't listen to critics. Dana Goldstein would be a much better one, or a couple of people at Brookings.