There are plenty of decent arguments in favor of bans of the burqa and niqab. For example, the veils are not actually regarded as religiously compulsory by 99% of practicing muslims and it coincides with patriarchal misogynist abuse. Taking this as a fact, one can regard the burqa and niqab as a practice similar to those of fundamentalist Christians (such as the FLDS) that are often met with prison time. After all, seductive salafist practices such as polygamy, cousin and child marriage can be easily banned in any jurisdiction if they are not already illegal - the least problematic ban from a cultural impact perspective would be banning the covering of a face.
Yet the face shroud could be thought of as a symbol of free expression in a free society. If the burqa wearer doesn't have free speech rights, then who does? Free speech is for bad speech, and if the burqa qualifies as speech it would indeed qualify as bad speech.
The problem with the argument of free expression in favor of the burqa is that it is completely nonsense outside of the boundaries of the United States. Many western countries do strongly regulate speech and choose to make a very big deal out of speech that Americans would not even blink at.
One of the countries that does seemingly regulate 'hate speech' in situations where the United States would not is Canada. There appears to be a lot of laws on the books regulating speech and a lot of precedent related to their usage.
If Canada, at a federal level or otherwise, is going to find itself in the business of regulating speech it must necessarily find itself in the business of regulating dress. It would make no sense for "hate speech" to apply to words but not deliberately provocative actions, like marching with torches while wearing klan outfits or swastika armbands.
Banning white hoods in public to dissuade racial discrimination may be a great idea or a terrible idea. The only mystery here is why the same logic could not immediately be applied to protecting women as a group by banning something as obviously negative to their collective well being as a full face veil. It could be that some 'inclusive' minded people do not see the veil as a problem as women appear to 'choose' it, but this is no more relevant than when clickbait provocateurs choose allies and iconography that clash with their own identity.
In a country with regulations of 'hate speech', it does not follow that problematic speech suddenly becomes acceptable if some subset of the impacted class somehow finds itself co-signing the discrimination. For example, one could assume that racist abuse of an ethnic minority does not suddenly become appropriate if a member of that same minority is the one spreading the discriminatory rhetoric. This is not a hypothetical scenario, as virtually every bigoted, sexist, racist, xenophobic idea manages to find an absurd level of agreement within the very groups they despise - especially in the weird corners of the internet. Humans are weird.
The only reason it would seem that the burqa is seen as a 'choice' is not immediately dismissed as traitorous self-hatred is that 'feminism' in popular culture is currently struggling with the idea that women do not currently have enough choices. Therefore, anything that would appear to add one more choice must be a net positive development. Under this banner, every kink is validated - everything from whips to wahhabism. The global context does not matter, as the progressive activist class is ironically 'America First' in both data points and mindset. Nevermind the real lived experiences of millions of women arriving in the west from backwards theocracies, the important thing is some poor soul born today to some helicopter parents in a western democracy gets to 'freely choose' to dress up like a niqabi ninja for the rest of xir life.
The burqa is a white hood, the burqa is a red armband, the burqa is a confederate flag, the burqa is dressing up like General Lee for Halloween.
So, does one really wish to regulate hate speech?