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But what really grinds my gears about (other) leftists defending this kind of religious expression is, this isn't something women choose.
How do you know that?
They're forced to and groomed from young age to cover themselves.
That's... kind of how all parenting works? You could legit say "they're forced to and groomed from young age to X" and replace X with anything you want and it'll work so you're not really saying much.
This is just plain old misogyny that has no place in modern societies.
Yeah here's the thing: Freedom of conscience means freedom of conscience, even when you don't like that conscience. If misogyny is reason enough for you to take a sledgehammer to this core pillar of democratic society then go ahead, but know that fascists can use that same sledgehammer against whatever beliefs you have that they don't like.