I believe in Teshuvos Binyan Tzvi there’s a teshuva regarding issues of bizui talmidei chochomim. If I recall correctly, the person asking the shayla found that at one shul he went to, they were mevazeh the other shul’s rov and said he wasn’t a talmid chochom etc etc, and the other shul reciprocated.
If I’m not mistaken the question was whether he could daven in a minyan in either location. The teshuva (as I remember it) says that because each community is doing it al da’as their rov, so nobody is posul l’minyan.
I hope I’m recalling this from the right location – I don’t have the shu”t on hand.
Just thought I’d share.