Do xtian laws specify that women wear tents with just a slit for their eyes as well?
Well.. having burkhas is actually a Christian tradition that Muslims started with after the fall of Constantinople. Because Constantinipolites/Byzantinians were well educated they got prominent positions in the Ottoman administration. So having a wife in a burkha became associated with having influence and power (in spite of their carriers being Christian). So it caught on (among the affluent). When they converted to Islam they kept their Christian tradition of having burkhas. The practice spread further, and even out into the provinces. No, it's not in the Bible either. It came to Christianity from Paganism. It was a Roman pagan tradition among upper class women, who were too fancy for the eyes of mere lowly commoners. That's where the tradition comes from. When they converted to Christianity they kept this tradition, as it signalled that they were upper-class, affluent, fancy and all that.
It wasn't all that wide-spread in Islamic countries prior to 1830. It was mostly a Muslim upper- and middle-class thing. It wasn't until the Muslim brotherhood got going in Egypt that full "Islamic" covering became an Islamic thing. It became about pride. It was essentially a competition of who's women was the most honourable, and the more skin that was covered the more honour. This was a wholly novel and new concept. But they modelled their dress on the Ottoman tradition, which I explained above was inherited from Christianity.
This is actually a pretty common theme with both Christianity and Islam. When a region converts they mostly just convert superficially. Almost all the rituals and traditions are kept from whatever they had before. There's hilarious descriptions of Mansa Musa the Malinese king who went on a Hajj to Mecka. He had apparently "misunderstood" Islam fundamentally which caused much consternation. He was the world's richest man at that point so they were in no hurry to set him straight or turn him away. He went home to Mali none the wiser. But all his lavish gifts of gold completely crashed the market for gold radically devaluing it. Lol.
Not to be confused with Islamic desert-dwelling nomads who are covered from head to toe in black robes for purely practical reasons. Also a tradition that goes way to before recorded history. Nor to be confused with the Zoroastrian tradition (today's Iran) who also had this practice for... reasons I've forgotten. But when they converted to Islam they kept the tradition of having Burkhas as well. This explains all the different varieties of Muslim coverings and head-scarves. One note though. The religious demand for women to cover their heads is pretty universal for any religion. Historically, extremely common. Was the norm in the west up until just a hundred years ago.
So basically... if there's an Islamic tradition somewhere to do something it probably was a tradition there to do it, way before Islam came to the village.