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).

And then you look at the actual rules (https://en.wikipedia.org/wiki/Popular_initiative_(Switzerlan...): "A double majority of people and cantons is required to change the constitution."

--> 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.