From what I have personally seen, the conservatives who are the most pissed off and have a real, personal experience in the matter are those whose kids come up to them one day, state they are trans and start asking to be called by different pronouns. These parents blow a gasket and look for someone to blame. The conservative info-sphere is right there ready to provide them with targets. These families talk to their friends, their pastor, etc... about the experience. The conservative narrative is reinforced by experiences conservatives have with their own kids, or with friend's families that they know.
Are these kids legitimately trans? In my opinion, knowing these kids, and knowing full well it's not my place to make such judgements, the answer is, pretty exclusively, no. So where are they getting the idea they are? Again, just from what I have personally seen, these kids are getting it from a combination of YouTube, teen gamer culture, discord, Minecraft servers, etc... They get it from their online hangouts, especially during lockdowns when everything else was shut down and kids were spending a lot more time than normal online. Places where it's "cool" to be trans and internet anonymity and disconnection provides a sense of safety.
You can get as tinfoil hat as you want after that. Is this just the 2020's equivalent of a teen coming home with a tattoo in 1990 much to their parent's chagrin? Or is there a strategic effort to influence kids online and engineer these feelings within them and the resulting rifts in U.S. families as a means to weaken American societal cohesion?
I dunno. The only thing I am certain of is that these kids sure as shit weren't groomed by the poor public school teacher just trying to not be an asshole when a kid came up to them after class questioning their gender because they know they could never talk to their conservative parents about it. They either go to private religious schools or are home schooled.
If a kid's ultimate life's happiness as an adult lies in being trans, then I want them to be trans as fuck and not have that right be imposed on. This is just what I have seen from conservative families with kids experiencing gender dysphoria over the last few years. YMMV.