I am repeating what I have heard from other Swiss people, so while you may not feel that the electoral system is as good as it should be (which is a completely justified opinion in any country and I am sure that Swiss people are not a monolith on this topic), it would be disingenuous to say that Switzerland is not even remotely close to a direct democracy. I am not aware of any other country that has a formal mechanism for laws to be changed where the government or parliament is not directly controlling the process.

> it would be disingenuous to say that Switzerland is not even remotely close to a direct democracy

I am saying it is as good as it is because it is not direct. The majority can propose an initiative, but the legislature gets to deliberate and draft a counter-proposal, with all of this taking time and encouraging sponsors to withdraw their initiative. In essence, it’s a way to prompt the legislature in a certain direction. Not for the majority to write the law. For an example of how that breaks, see California’s referendum process.

And also, from my understanding a local Commune doesn't have the power to overrule national laws locally. Which means that when a short majority of racists sets up bans related to muslim cults as happened a few years ago, a local municipality can't overrule that and say all faiths and buildings and clothings are welcome.

Is my understanding correct?

> a local Commune doesn't have the power to overrule national laws locally

Yes, federal law has general supremacy.