To demand public humiliation doesn’t just put you on the same level as our medieval ancestors, who responded to violations of social norms with the pillory - it’s actually even worse: the contemporary internet pillory never forgets.
Shame is also not the same thing as "public humiliation". They are publicly humiliating themselves. Pointing out that what they publicly chose to do themselves is bad is in no way the same as coercing them into being humiliated, which is what "public humiliation as a medieval punishment" entails. For example, the medieval practice of dragging a woman through the streets nude in order to humiliate her is indeed abhorrent, but you can hardly complain if you march through the streets nude of your own volition, against other people's desires, and are then publicly shamed for it.