Dear Shnitzel,
Hilchos Shechaynim is predicated on being able to have some dialog with your neighbors. You could take money from someone to pay for your damages. There is no payment for making to much noise etc. Therefore, the first enforcement is being able to negotiate terms.
The main concepts of these sugyos are that the physical effects of my property cannot extend into your property, but my nonpossessory extends to your property as much as it is a right and not a monetary benefit. Subsequently it is very dependent on the norms of the neighborhood in question.
In regards to a shul or beis medrash, one can object to using the house they live in. If it is in a different house, even on the same property one cannot oppose it. NIMBY does not apply to shuls and schools. However, if someone is using this halacha to exploit the neighbors, the Rav is required to stop them.