"And what is it with disgruntled parents that they compare shoe shaming to the racial policies in Germany of the 1930’s and 1940’s?"

They're not comparing it to the racial policies of the Third Reich. They're comparing it to the Authoritarian (we have the right to tell you what to do) and Totalitarian (no detail, however small, is outside our control) practices of that Regime.

To quote Hitler:
"That is the great thing about our movement... that these [SA] men have outwardly become almost a unit, that actually these members are uniform not only in ideas, but that even the facial expression is almost the same."
Speech at the Sportspalast in Berlin, 10 September 1930

Nothing about race in that speech or attitude. It's all about a desire for control and enforced conformity. Pretty much exactly the attitude being exhibited here. Something those who stayed awake — or, at least, payed attention and retained what they learned — in their history classes would understand.