There is a big risk that, as you say, parents who can't deal with a gay child, and parents who are disappointed in the sex of the child they have got will encourage them to think that they are 'really' of the opposite one. We know that in countries like Iran it is 'allowed' to be transgender but not to be gay. I don't know how that link is made, but it is clearly there for some, as numerous boys in Iran 'transition', and even here there is a lot of confusion between sexuality and trans issues.
I also think that there is a world of difference between children transitioning and TRAs imposing men who have simply declared that they are women into female spaces, and insisting on changing the language. Both have problems, but IMO the TRA ones are problems for all of us, whereas the problems for the transitioning children are likely to stay with them.
I would also question the validity of the piece. The study may well have had those findings; but it is the author of the 'news' story who makes the link between the study and the fact that some states are banning the use of puberty blockers and other medication for young children. I have never heard of the author, but if she's the Julie Mazziotta that shows up on LinkedIn, she seems to be an 'expert' in a remarkable number of topics, none of which have involved an education in health-related topics. Her degree was in Politics ?