I can't speak to democratic/republic, but a number of syncretic religions and alternative spiritualities are either decentralized or so fragmented as to be functionally so. In my experience, such provide several of the social benefits of religion - i.e. gatherings of like-minded people with shared theologies - with reduced potential for abuse of power.
Of course, the scalability of these systems are unknown.
Of course, the scalability of these systems are unknown.