True, Switzerland (who I view as a "green" and progressive country) recently voted against those taxes in a referendum. I think it would be much worse in other countries.
Switzerland, like California, is a direct democracy. Taxes that touch the assets of voting demographics fail while taxes that burden non-voting demographics pass.
Nit: Switzerland as a country is a semi-direct democracy not a direct democracy. Only 2 cantons fulfil the criteria for the classical definition of direct democracy.
Indeed, Switzerland is very conservative. Like in every other country you have a divide between the progressive/liberal/young-ish big cities (Zurich, Bern, Lausanne, Basel, ...) and the conservative/old-ish rest of the country (great skylines, very low population density).
--> Swiss cantons are split up historically, not by population, similar to US states. The conservative, low-pop cantons can hold the progressives hostage on anything they don't like because even if you get the liberal cities behind you that is still way beyond the majority of cantons.
Comment you're responding to probably didn't mean American conservative. Most conservatives support abortion in the EU, it's the far-right that doesn't.
https://www.bbc.com/news/world-europe-57457384