Why do many conservatives paint the entire public school system with a broad brush?

Shame on you for insinuating such a fine and upstanding institution would utter any untruth! You even provided proof that they’re telling the truth. They don’t discriminate in policy. Now, of course, it’s a quite different story as to what they do in practice. For example, from the Wiki link above:

In 1989, the school forfeited a football game to Heritage Academy because the other school had a black player.

This is one of the many reasons I advocate first for school sports to be treated just like any other school club. And if a school cannot manage to do that, then they need to no longer have a school sports club. If a community wants to have a yourth league, do like so many bowling alleys around the world do: the alley/ballpark/stadium organization sponsors the youth league. If someone decides to go against the league rules, then bye bye to the team. No use of public funds for this nonsense.

I’m in no way defending this school, but here in Dallas some of our most progressive private schools started as deseg academies.

Fifty years ago, wealthy white parents in the city wanted their kids to go to entirely white schools. Now the urban elite lean left, so they want a mostly white school with a substantial, but not overwhelming, number of historically disadvantaged minority students, but only ones that have been carefully vetted.

It’s better, but not good.

“I don’t like the city parks. I want to join a country club so my kid doesn’t have to play with ‘those’ kids, and I want the city park system to pay for my membership. School vouchers in a nutshell.” (Stolen from social media)

The older generation fears a younger generation.
It will fear them less if the younger generation believes as they do.
That is more likely in a school that teaches the way and the things they learned.
That’s a private religious school.
Tax payers don’t pay for indoctrination.
Nor should they.
Nor would even the most hardcore Christian want a dime of their taxes for Lil’ Tykes Madrasa to prove a point.
And the sharper conservatives knew this so kept the sabre rattling to a minimum, bring it out to harm the teachers union or pressure a school to watch bathrooms instead of care about gun safety.
But you stir crazy in a group long enough and then they want something DONE, no more talk.
But there isn’t a solution except destroying the entire education system as we know it.
So here we are in a holding pattern until someone decides what they want to have really happen.

As just a data point, my parents are very liberal and yet I would say they are becoming afraid of how children are now growing up. Their friends feel this way as well. If they believed ‘school’ was the problem they would act.