Wolf, someone who cannot give tochachah in such a way as will
cause it to be accepted is patur from that mitzvah. I don’t
see why you’d be obligated to refrain from davening in that shul,
unless you just want to avoid conflict with that Rav, or halacha grants
Rabbonim the right to decide who may or may not daven in their shul,
regardless of whether they are doing or have done anything wrong.
I always assumed that the Rav of a shul had the power to ask people not to daven there. This particular Rav certainly believes he has the power if he can ask people who cannot or will not follow his conditions not to daven there.
The Wolf