Those church-only parties are fascinating. Do they campaign in the same way state-based political parties do, with manifestos and membership and branding? Or are they really just informal "nomination groups"?
They're probably more active in campaigning than the main parties, which admittedly isn't saying much for Church elections.
It is worth noting that many of these groups are in fact strongly connected to "ordinary" political parties, who have decided not to participate in Church elections in their own name out of principle, but whose groups still continue under new names with the party's informal support. So the Bourgeois Alternative (which sounds less ridiculous in Swedish) is connected to the Moderates, the Free Liberals are connected to the Liberals, and so on. The only truly "Church-only" groups are the Open Church (liberal, left-wing), Outspoken/Fearless Church (very, very conservative - their slogan is "a church that dares to be a church"), and POSK (which has members across the political spectrum, and stridently maintains that it's not a party, just a loose association of people who want to be elected without participating in party politics).