but even the most devout young Muslim must surely feel alarmed at things like being forced into a marriage when, if that identity were split, they wouldn't have to be
Fourmummy, your ignorance is painful.
Forced marriage is as forbidden in Islam as eating pork.
It is documented that a woman approached the Prophet Muhammed (pbuh) to complain her parents married her off without her permission and he told her she could get divorced instantly.
You didn't know that, did you?
Forced marriage is a cultural issue and culture is not the same as religion.
SamG upthread quite rightly pointed out that your planned "no religion outside of the home" would not be tenable for most faiths.
You declare that a Sikh man can only wear a turban at home, do you know why Sikhs wear turbans and why it might be extremely impractical for them not to wear a turban?
What about Rastafarians and their dreadlocks? Would someone have to hide them, or would it be that they could only be worn for "secular" reasons?
Then there are beards. Would Muslims, Sikhs and Jews be forbidden from growing beards and forcibly clean shaven?
If I choose a vegetarian meal in a restaurant, because halal meat is not available, is that mot allowed either, because I'm practicing my religion outside of my home?
Btw, the even quite recent history of many religions shows there was a time when they had to practice in secret and yet they are all still with us.