Sorry but it seems like both sides are being insanely hard headed about this Burka/Hijab ideology.
Let us simplify maybe to find common ground?
Women should have the Freedom to wear anything they want, if a woman WANTS to wear clothing that covers literally every part of them from head to toe, then Amen, go for it.
If a woman wants to wear a bikini that barely covers anything (as long as it doesnt amount to literal indecency aka nudity) while I personally oppose it and would rather them cover themselves and dress modestly, then since they are not breaking the law by doing so, go for it.
However once there is ANY type of legislation, by any governing body, whether Political or Religious that mandates a certain dress and then ENFORCES a punishment, then at that time, the type of dress is no longer about freedom but about force.
And THAT is the problem people have with the Burka/Hijab, because in MANY Countries and throughout MANY communities that have a Majority of Islamic followers, the dress becomes a LAW and MANDATORY and then is ENFORCED via threats and violence or rejection from the community all together.
If the same thing was happening in Christian/Jewish/Pagan households EN MASS throughout the entire world THEN you would see an uproar from people in the same fashion that people have uproars over Islamic dress.
With that said in AMERICA where Freedom is still a thing, if only by a slight margin atm, if a Muslim WANTS to dress head to toe in black, even when its 100 degrees out, then by all means GO FOR IT. I support and stand behind your decision 1000000000%.
However if that woman is doing it because she is afraid her husband or community is going to either hurt or ostracize her then I would 10000% stand behind that woman to be allowed to dress how she wants WITHOUT threats or intimidation.
The problem however, is that in many communities the women do NOT have the actual choice and would have to endure violence or ostracization for not conforming to the dress that is being mandated.
So here is the common ground.
Let women dress how they want, and make it WRONG to FORCE them to don a Burka/Hijab if they choose NOT to do so. However that is an extremely hard thing to mandate because Culture is more persuasive than Laws, and if they come from a Culture that enacts violence or any other type of negative reaction to not wearing certain clothing, then those women will remain oppressed.
And to be clear, there is a Law in some countries in Europe BANNING the Burka, and I personally dont agree with them, the Burka or whatever other Islamic Attire should be legal...