"Hey guys we're polling really poorly with women after we stripped them of their rights in several states. How can we smear this guy to gain back ground?"
"Let's highlight how he made schools provide menstrual products to children that need them. That's a bad thing. Women won't like that."
Yeah, but only because they had to really stretch to manufacture outrage.
"The products must be available to all menstruating students in restrooms
regularly used by students in grades 4 to 12 according to a plan developed by the school
district"
That doesn't scream "pro-trans". It certainly allows for it, but the wording is so neutral that you really have to be thinking to explicitly hate on trans to think this is explicitly out to support trans people.
The Terfs seem to mostly concerned about biological men in the woman's room, I don't think they will even care that tampons are in the men's room as long as they are in the women's room as well.
Eh, that's fair. They tend to have some small upset about trans men insofar as trans men make trans women more socially acceptable but you're right - the primary target of TERF anger is trans women being in women's spaces because they believe trans women are men, all men are predators, that the purpose of women's spaces is to keep women safe from predatory men, and that trans women being a thing essentially allows predatory men to put on a costume to gain access to victims in vulnerable positions.