I am looking for story in which the characters are living in a commune but men practice polygyny using religion or politics as excuse. Something akin to FLDS, a group of people living outside the reach of law. Time period doesn't matter. But males should be adult, not teens.
I read a book with such characteristics. If allowed, I'd post a goodreads link to it.
https://storiesonline.net/s/58589/dark-days may possibly fit your criteria, I'm not 100% sure since it's a long time since I read it.
If SF works, how about Arlene and Jeff by RoustWriter? The "Florida Friends" series by Dual Writer?
I think it would be a stretch to describe either of those stories/series as male-dominated and for religious or political reasons.
The Preacher Man by hammingbyrd7 is more religious in nature, but it's not "outside the reach of law"; it's part of the social order.
"outside the reach of law" in a normal universe. A universe which has it as part of a social order is fine with me.
This is the book that I am talking about in my post: https://www.goodreads.com/book/show/30749420-the-sister-wives-of-concordia
In DotB's Car 54 they have a run in with one of the more radical FDLS breakaway groups. It isn't the main plot line but it is an important sub-plot that comes in about halfway through.
https://storiesonline.net/s/46723/car-54
I have two suggestions, neither being an excellent fit to the presumed requirement but both within the letter of the request, provided a fairly loose definition of commune is taken.
First, Gina Marie Wylie's Will you do this for me?
Second, a dead-tree rather feminist novel Sheri Tepper's The Gate to Women's Country.