https://en.wikipedia.org/wiki/2011_Wisconsin_Act_10#Effect_o...
"the law reduced average test scores on the state’s standardized exam by approximately 20% of a standard deviation": https://www.sciencedirect.com/science/article/pii/S027277571...
"8 percent reduction in total compensation" https://www.cato.org/sites/cato.org/files/pubs/pdf/rb71.pdf
Not only does this hold up in general, it holds up district by district. Districts that still had collective bargaining had better scores than one that didn't (even after controlling for confounds, it was the union status that made the difference).
https://journals.sagepub.com/doi/abs/10.1177/0160449X1988337...
Not only that, teacher shortages are worse, and they're much worse in rural areas.
https://search.proquest.com/openview/5ae518d77f9e44551206208...
So the outcome is: Teachers make less money, there are fewer teachers to be had, and students are scoring much worse.
A win-win-win for conservatives!
The Catholic schools' policy on things like this, at least near me, is dictated mostly by the diocese. The state can withhold funding for things like special-ed programs or meals if they won't play ball, but they get more autonomy as long as they aren't violating civil-rights law.
The teachers' union does. Not most of the time either. All the time.
Additionally, you don't have public sector or really any teachers unions to deal with at private schools.
There are other factors that contribute, but aren't nearly as clear cut as those two.