There is, obviously, no reliable way of knowing how much compulsion is involved,

Exactly. This doesn't show in your words though, where you always assume compulsion, not free will.

It's your theory that the headscarf is necessarily about a girl's "worth" or assumptions about her sexuality (sexual behaviour). Sometimes it is a statement about her regional roots or a statement of defiance in the face of discrimination. More often it is a statement on sexuality in the sense of physical integrity. Even where it is a statement about restricting women's roles, this message does not need the headscarf (or the pleated skirt in my childhood which symbolised exactly that). Parents who teach their daughters that their place in life is a subordinated one, may choose to impose certain clothes, but these clothes are only a symptom).

My point with the pleated skirts is that the same sexist views that you say you fight by a ban on headscarves exist among the natives too. You still choose to fight the headscarf, and that makes your message morph to something like "sexism is a Muslim problem." That is not only playing into the hands of Islamophobes (I hope I have found a wording that doesn't make you explode again) but into those of native sexists too.