INAL but I don't think this has a lot to stand on, regardless of being for or against the actual policy.
I think similar cases would be for following various federal laws to receive highway administration funds.
Florida can still run their schools, it doesn't challenge state law.. they're allowed to fund them themselves. So doesnt involve 10th amendment here IMO.
The question will be about involving non-government agencies in doing the accreditation.. which one could argue would have similarities to defense contractors (maybe?) I don't know what precedent exists on this angle.
Given current supreme court is corrupt enough that who knows what will happen if it makes it's way there.