No, actually it's the only place that's somewhat democratic.
In fact, patriarcal is more likely a good adjective to describe the anti-foreigner areas. For instance, one of the highest votes for a recent anti-immigration referendum[1] was in Appenzell Innerrhoden. That same (half)-canton only gave women the vote in 1990, and only because they were forced to by the Swiss Federal Court [2].
[1] https://fr.wikipedia.org/wiki/Initiative_populaire_«_Contre_... (in French, but look for AI under "Par canton") [2] https://en.wikipedia.org/wiki/Women%27s_suffrage_in_Switzerl...
Funny. Do you know anything at all about Switzerland? (hint: it's a very patriarchal society)