It's interesting that your illustration illustrates your point in an important way, something probably worth talking about.

That photo of East Berlin parents burning books was taken by a press agent of the government of the German Democratic Republic (East Germany), an authoritarian regime that spied on and oppressed its citizens, strictly stage managed public events, and ruthlessly repressed any genuine public protest or manifestation.

The parents in that photo were there because someone in the East German government told them to be there and told them exactly what to do. Of course, the government was not comprised of Nazis, quite to the contrary. East Germany was a Warsaw Pact satellite state, strictly beholden to the Soviet Union, another authoritarian regime that tried to control almost all aspects of people's private lives.

In the Soviet Union, and by extension in East Germany, privacy as a concept of liberty did not exist. Private lives were presumed to be part of the political sphere, subject to state control, enforced by harsh criminal penalty.

The difference between Communist and Nazi in this respect was not significant. Overarching economic philosophies were not what mattered. State authoritarianism mattered. Strict control of private lives mattered.

Republicans today, including members of Moms for Liberty, consistently praise authoritarian regimes like Russia and Hungary, expressimg admiration because the governments of those states demonize and harshly oppress queer people.

That's the kind of state Moms for Liberty wants, a state that wields authoritarian power to enforce their own (mostly religious) ideas about repressing queer people, Black people, and immigrants.

The "moms" say they support parental rights, but they don't. They support authorization government repression of parents who don't share their religious values.

And the far-right GOP establishment is throwing tens of millions of dollars at them in support.