There is a huge overlap between the "I want tax dollars to fund my religious ideology" and the people who say "lgbt kids should be punished", "sex education must be banned", "teenagers [girls] who have sex should be shamed", "child marriage is acceptable", etc.
All of those policies are inherently pro-child abuse.
Those are the same groups that also say "my religious freedom requires that I be allowed to require other people to follow my religion.
The only reason conservatives want publicly funded private schools is because they want to claim that the schools are (1) not public so don't have to obey the first amendment and (2) then reduce funding to actual public schools because they "can't afford it".
Anyone who claims otherwise is at best stupid.
This is the explicit intent of these policies.