What I admire about the Swiss is how they live and let live - they may disagree with the neighbour, but let them be.
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.
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.
The Swiss rule their house, and let others rule theirs, and this is what I mean with living and letting live.
My point is that while the majority of Swiss cantons decided to not have gender restrictions on voting, they allowed Apenzell to keep being the weird one, and in response the people of Apenzell don’t force their way onto others. If I don’t want my neighbour to tell me how to run my household, I must also not force them. Apenzell didn’t force their way into the Züricher.
Although in the end, the people of Apenzell were forced to change their way.
