Well, it's a very modest thing, and not (to my knowledge) offensive to God or the Faith... Women have in history worn veils and such modest attire and have been Catholic. Unless there is something about doing it which is a direct profession of their faith (like genuflecting is to adore the True God), I can't see the problem. But of course I'm also very ignorant on this particular subject.

In Africa, there was recently a little outrage because the Church there demands converts to destroy ceremonial goods and idols "linked to their heritage and culture, and of historical significance." But in that case you're talking things that are used in sinful "worship" or which have had "curses" or "spells"  put on them, and idols which of course directly violate the law of God.

As for the significance of this way of dressing, my uneducated guess would be, if it is linked to the worship of a false God or the errors of a false religion, I would guess it would be harmful and therefore ought obviously to be forbidden. If it's just done for modesty's sake, and because a woman "should not have her head uncovered when she prays/in church" like the Bible says (even if we don't observe this outside of church ourselves), then I can't see anything intrinsically wrong with it.

Of course again, I am just making uneducated guesses here.

looks similiar to how nuns are meant to dress, and how Our Lady is always depicted as dressing, I would imagine the early Catholic women dressed in this way.  It also seems more inline with the wishes of St. Paul.

1 Corinthians 11:

5 But every woman praying or prophesying with her head not covered, disgraceth her head: for it is all one as if she were shaven.

6 For if a woman be not covered, let her be shorn. But if it be a shame to a woman to be shorn or made bald, let her cover her head.  

Some things found in a culture to be Catholicized would indeed have to go though if they were found definitely contradictory to the Cathoilc faith.