Religion-based parties ? Out of the large parties, only the CVP is religion based as it is the successor the old KK (Katholisch-Konservative Partei), and out of the smaller parties, only the EVP (Evangelische Volks-Partei) is religion based. All the others are not religion based.

State-religion ? While some Cantons regard the dominant denomination as a kind of state-religion, the union does not. And even in the "religious" Cantons, you can write a letter to the Church and declaring that you now have left their Church and declare "religionslos" on the tax-forms and then you no longer are paying for churches and priests. So that legally, neither unions nor cantons nor municipalities have "state religion".