actually, the tradition was to wear a head covering. Yidden were secluded from goyish coulture in the previous few hundred years due to goyim forcing seclusion. Since the time of the churban yidden have lived with goyim and in times held high positions within governments. If yidden were so secluded, why would there be discussions in the gemarah on how to build an eruv whe a goy owns a house in the chatzer, asking a goy to do melacha on shabbos etc. This seclusion is an outcrop from the dark ages when it was thought the jews had heebie geebies. It also didn’t help that every few decades they goyim decided to go on a jewish killing spree.
If kids were actuially taught the halacha and the beauty in it, some problems would disapear by themselves. If someone is mechalel shabbos, yelling in the street shaigetz does not help. If the person is taught hilchos shabbos and the rationale behind them (not because g-d said so) there is a infintestinal better chance of seeing the behavior change.