... Parents are supported in forcing any type of ideology down the throats of their kids, and insisting they live that way, as long the consensus opinion either supports it, or isn't too offended by it despite whatever misgivings the consensus may have about it. However, if consensus opinion finds the idea thoroughly offensive, even if no proof or good evidence can be found that the idea is in any way harmful, they will be virulently intolerant of it.
A good recent example is the Miley Cyrus debacle. Consensus is heavily against any remote possibility of perceived exploitation that might entail a sexual aspect due to stated concerns about harm. However, it fully approves or at least tolerates the infliction of harm based on extreme suppression of something perceived as a sexual expression from someone who is seen as "too young" to express that part of human nature -- even if said suppression includes a vicious campaign of shaming and harassment to manipulate said young person into being forced into a public apology. This is due to society's heavy anti-sex bias, one that our society does not like to admit that it still has.
The bias also extends heavily into semantics. For instance, I believe the consensus opinion would indeed weigh heavily against parents raising their kids to be Neo-Nazis, in the sense of spouting classic Nazi rhetoric, and using Nazi-associated jargon and symbols. However, if you express very similar rhetoric and ideology that is instead wrapped in the cloak of the stars and stripes of the American flag, and using American symbols and phraseology, then the matter is entirely approved. That extends to the actions of American allies like Israel being given a free pass for its government's actions against the Palestinians, totally ignoring the disturbing similarities to what Nazi Germany did to the Jewish people in the past. This also ties into the SJW mentality that former victims and formerly oppressed groups automatically earn the moral capital to behave any way they want towards other groups of people, as long as that behavior focuses itself on either groups who were oppressors in the past, or who had never acquired "perpetual victim" status in the eyes of American consensus, or if they happen to be citizens of a foreign country that is currently on America's shit list.
In other words, Americans -- including liberals -- are against or supportive of fascism depending upon which group or nation is the target. Different groups of people are held to different standards of behavior. To them, blowing up a Jew or a homosexual does not carry the same moral equivalency to blowing up a Palestinian or a heterosexual, respectively. Mindless hatred focused upon all women (misogyny) carries a different moral equivalency than mindless hatred focused upon all men (misandry). Attacking Russia, a country America is currently bickering with, does not have the moral equivalency of attacking Saudi Arabia, one of the most brutally oppressive and misogynistic nations in the world, because its ultra-privileged ruling family -- which has far more influence on American business and politics than Russia ever could these days -- is on good business terms with the U.S. government, including centrist Democrats like the Clintons (patriotic liberals will not approve of what the Saudi Arabian government does, of course, but they will never talk about it, instead keeping their attacks focused on Russia).