It isn't splitting hairs at all. You are suggesting that the wearing of burqas in public is a serious threat to national security. However, you have failed to produce any evidence whatever of this. There are many different ways of covering ones face, and I agree that all forms of restrictive headgear should be removed in certain cirumstances. However, it is a very drastic step to move from asking for, justifiably, equality in certain areas (entering banks, for example) to demanding a ban on specific items of headgear ostensibly because they are a threat to national security.
In the case of the burqa, it seems that a badly-thought-through correlation has been made between "Islamic item of clothing" to "terrorism".
I'm all in favour of preventing women being FORCED to wear it (though I don't see how that would be enforceable). However, simply banning it would make life pretty grim for many Moslem women, as many would probably be trapped at home.