I think a lot of analysis people put forward on this is completely fucking wrong. It's not really projection, it's strategic and carefully thought through by far right strategists and thinktanks who are the real vanguard of the far right movement.
The tactic is about tapping into deep seated insecurities that people have and weaponising those insecurities into tools of the movement.
Most of this has been about targeting people who are 40+ in age. Everyone above a certain age threshold can see very clearly that younger people have a drastically different worldview compared to them. This needs answering within society otherwise these people will be forced to come to terms with the fact that Gen X and Boomers had drastically different material conditions that resulted in their massively different views compared to Millenials and Gen Z.
Bring in the grooming myth. Young people are gayer and "woke", why? Because the left has GROOMED the youth via academia and WOKE IDEOLOGY.
You explain away the differences of views in society and you weaponise it into a PROTECT THE YOUNG tool. This turns your reactionary movement of proto-fascists into crusaders that believe what they're doing is good and right and for a good reason.