I think the issue of private schools asking gay children or trans children to leave is not as plain and simple as one might think.
You think the school is behaving in a bigoted way, but would you say an Islamic school is wrong to ask girls to cover their heads? How about an orthodox Jewish school that won't serve non-Kosher food. Accommodation where possible is optimal, but it is pretty hard for a gay or trans child to attend a Christian school and not hear their behavior is sinful according to the religious beliefs of the school.
The parents of the gay or trans child who send their child to private school should really ask themselves why are they doing this to their child? That is the real question you should be asking. Is that really healthy for the child? It almost appears to be a form of child abuse.
Nor should the parents demand the Christian school not preach its values, since that is the primary reason why most parents dig deep into the pockets to pay for the child to attend a private school.
If parents don't realize the stress that such a situation creates for a young gay or trans child, then shouldn't the school administration step in and address it. What if the parents are hoping the school will "fix" their child? Is that really something schools should do? If such behavior is "natural" and somehow genetically based, is the child going to end up repressed? There is more to the story, than you seem to realize.
Regarding Covid 19 outcomes, Florida has fared extremely well relative to other states. Meanwhile, more and more studies are confirming that requiring vaccines or masks can be counterproductive.
As a retired health care executive, I fit in the class of people that should get vaccines (I don't need to be told I have to get one). I have had five including the recent vaccine. But I am aware and willingly take the risks that getting vaccinated creates (a recent study identified "blood clots" as a risk factor for seniors). If I get a stroke, then that is the risk I took to moderate the risk that I die from Covid. Again, speak with your physician about the risks and benefits of getting vaccinated, if it makes sense for you... then you should get vaccinated.
As the Covid adverse events database identifies more and more unintended possible side effects of the vaccine. The initial decision to push for everyone to get vaccinated is being replaced by more selective criteria. Meanwhile, the CDC has come out and said, vaccination has done nothing to prevent the spread of Covid (which was the basis for the mandate).
Regarding masks, unless the regulations mandate the proper use and type of mask that needs to be worn, they are simply virtue signaling and there is virtually zero evidence of mask mandates reducing Covid spread (as the CDC has now acknowledged). When you view the "fashion foward" masks the Pelosi wore, it should have been obvious that masks were a fashion accessory, not a preventative health action.
If someone at high risk chooses to wear a mask (properly fitted of the right construction), then it can benefit them, but the mandates don't require that. Nor will healthy people comply.
So, if mandates don't work, why do you feel that DeSantis should allow local governments to encroach on the civil liberties of their citizens? Now if DeSantis said health providers can't provide free masks or vaccines, that would be different, but simply preventing localities from issuing mandates that violate civil rights without any evidence that they provide a public health benefit is the job of governors and the President for that matter... and as a last resort the Supreme Court.
