the doctrine says a believing woman should cover herself.
So when Muslim women begin to cover themselves, it is a visible signal of increasing orthodoxy. In other words, if there are Muslims in your area, and the women start covering themselves, it is an indication that the Muslims in your area are beginning to take the written doctrine more seriously.
And it is never just that particular written doctrine only — it is all the written doctrine, which includes hatred toward non-Muslims, political action to put the reins of power in Muslim hands, increasing demands for Islamic standards of dress, behavior, Islamic limits on free speech, etc. Because of the political nature of Islamic doctrine, these Islamic standards are not to be only applied to Muslims; as Muslims gain political power, those standards are to be applied to everyone.
Already in some parts of European countries where there is a high Muslim percentage, non-Muslim women are harassed (or worse) if they don't cover themselves.
Many of the signs of increasing devotion to Islamic ideals cannot be seen by non-Muslims. But the hijab can be seen by everyone.