Firstly "accepting a law" implies - in western liberal democracies - a legislative process in which a law is proposed and accepted by some kind of parliament. This is not what happened here - in Switzerland, laws can be given to the population directly by non-parliamentary, non-governmental organisations in referenda, which then become binding. The law you are referring to was accepted by the general Swiss population with about 51% of the votes yesterday.
2. The law is not specifically forbidding women particularly forbidding to wear burkas. It forbids anyone to hide their faces when in public (with the exceptions of traditional customs, e.g. during carnival season). The basic idea behind this is that in a free society, we meet each others face to face. This generally good idea was abused by right-wingers to point out that this prevents visible Islamisation of an ultimately christian-conservative country, and by left-wingers to imply it was sexist and islamophobic.
3. Men and women can still wear whatever they like ... in private. In public, all societies have acceptable clothing standards. Try going out wearing nothing but three straps of leather and a gimp mask in front of a school, anywhere in the world, and see what happens.
A little tyranny of the majority is not always a bad thing.
You can read this in a positive light or a negative light. I know a guy who had that surgery done as an adult and it was incredibly painful and took a while to fully heal. I want to say it was almost a month. You could certainly argue that it's a lifetime of pain if it's done and you don't like it but that's likely a slippery slope in some regard.
I can agree that we should probably be doing a better job of explaining to parents the pros and cons of each so they make more informed, realistic choices but some of the outrage rhetoric around circumcision is a bit much.
Medical science is very clear about both male and female genital mutilation: lots of risk and potential harm, not real benefits.
And this does not grow back like nails and hair. It's not a fashion. It's literally putting a knife in your baby because some old culture prescribes it. No problem with that: just do it when the kid reaches the age of consent.
Freedom of religion may not constitutionally compete with bodily integrity (nor with freedom of expression (blasphemy)).
This is more of a tangent, but I would contest the idea that "accepting a law" implies that it is passed by a parliamentary body. This was maybe true in the 1800s, but not today when plenty of western liberal democracies have some form of direct democracy with electoral referendums on important issues. Some (e.g. California) have a system roughly comparable to Switzerland, although it's obviously at the state level in the case of CA.
Imho that was the deciding part.
If it's the latter, that's a reason for them to seek help from the authorities.
The Swiss rule their house, and let others rule theirs, and this is what I mean with living and letting live.