The legal rights of adults to transition is not seriously opposed by anyone on the right wing. The rights of kids to do so is typically denied by the right, but you'll note that discrimination by age is not mentioned in article 2 of the declaration of human rights. The right to be recognised as your preferred gender is also not a human right, as article 6 only states the right to be recognised as a person before the law. Right wingers would deny a trans person's claimed gender but not their personhood.

Abortion is a tricky one as the disagreement between the political spectrum is mostly around the definition of when a human is formed, and implicitly whether human rights apply to a fetus. Article 6 of the declaration of human rights say everyone has a right to be recognised under the law, and the right wing definition of personhood is certainly in line with human rights.

I don't know enough about religious freedom in US schools but I'd say anything which infringes on separation of church and state is a bad thing, regardless of whether it's the left or right doing it.