Are you talking about a hypothetical place where schools are self-funded or something, or are you talking about Florida still? It's not that much of a free market if conservative-friendly charter schools get subsidized by the state but LGBTQ friendly schools don't.

Because local government has the power to collect taxes. If it chooses to selectively hand them out only to favored political institutions, then in practice this means many students won't be able to afford to attend their favored schools, and some schools will be financially non-viable. It may be the case that such schools will still exist in this environment (with a smaller student body), but that doesn't make the issue less problematic.