I've seen this claim and found it ridiculous. Giving the right wing nutjobs a benefit of the doubt, I tried to dig into how true it is. From what information I could gather, this claim is only prevalent in right wing echo-chambers. Out here in the real world, the facts are a bit more nuanced. Two examples I vaguely recall from my digging;
1. Some state (California?) allows teachers to use pronouns the student requests. They are not required to notify the parent when this happens. To a sane person, this is no big deal. If Richard wants to be called Ricky, does the teacher actually need to contact the parents? Like the preferred name, basic assumption is that the parents are already aware of the child's preferences. If the home environment is so hostile such that the child does not want to tell his parents, THAT is the problem, not the preferred pronoun. In such cases, it is in the child's best interest to protect them from the said hostility. The question such parents should be asking themselves is why the child is afraid to tell them, not asking the teacher to butt into their affairs.
2. In a certain contrived situation and sequence of events, it is possible for medical intervention to begin with one parent's consent but before the other parent can be notified. It would involve one parent to take the child to a more permissive state (one that has both-parent notify/one parent consent, rather than both parent consent). The more permissive state would begin the paperwork to notify the other parent's state, which in turn can notify the other parent. This could take a couple of days to go through. In that time, the child would have to go through all of the preliminary assessments and such required for start of treatment, get the appropriate appointments, and start the treatment. Needless to say, this has never happened to anyone's knowledge and is extremely unlikely to happen due to the time it takes to go through all of the steps for starting such treatment.
My conclusion is that all this noise is contrived to manipulate the gullible into voting against their interests. It is not a significant problem for most people making a big deal about it. The number of people directly affected is fairly small, and really, it should be their problem to deal with. At the political/population level, there are much bigger fish to fry, like a sane foreign trade policy.