I used to think shuls should accept everyone however recently 2 individuals occassionaly attend my shul have made me change my mind
One has been accused of certain things (bur not convicted) that could put the safety of children at risk. Thankfully he does not live in the neighborhood, but was considering moving. When he comes we closely observe him and if he would move to the neighborhood and join our shul I would strongly object to him attending
The other who does attend semi regularly is a bit off and behvaves strangely and sometimes a bit menacing . I know the Rabbi is watching him closely