If I am a member of a shul, must I follow all the halachic rulings of that shul’s rabbi? Am I entitled to go elsewhere for guidance on halachic issues (such as this website)? If I am a member of more than one shul, which (if any) of the shul’s rabbanim am I obligated to follow?
There is no obligation to follow the rulings of any specific rabbi, unless you have accepted him upon yourself for all matters of halachah.
In previous times, each place has its own central rabbinic authority or rabbi, and the local rabbi’s decisions would be binding for the relevant community or city (see Rashba 1:253; Rivash 256; see also Chazon Ish 150:8).
Today, we live in a time when central halachic authority is no longer binding (see Mahari Ben Lev 1:75, who notes that even in his time the concept of a central rabbinic authority could not longer be upheld).
Although for shul or inner-community matters the rabbi’s decision will of course be authoritative, there is no obligation on congregants to accept the rabbi’s authority in personal matters, and they can turn to whichever authority they deem credible and worthy.