Generally, we know that if a Jew were to move into a new Jewish community, they would take on the local customs of the community as told. I am curious as to whether Noahides have the same obligation, so if a Rabbi of a local community accepts a Noahide and they move in and are allowed to be in the synagogue and everything else, do they also halachically have to do whatever local custom is set, like e.g. monogamy in Ashkenazi communities?
Yes and no. A good Jewish way for a Noahide to answer that, right?
No, Noahides are not obligated to take on the community customs in the same manner as Jews. The Noahide's scale and scope of participation in Jewish lifecycle events will always be different that the Jew's.
However, the practical side of it is that yes, the Noahide does have to take on some of the community customs, in so far as he wishes to be a proper part of that community. For example, I studied with a rabbi in a community that uses the Sephard siddur from Artscroll and that is what I had to use while I learned from him. I wasn't obligated, per se.
It's important for Noahides to be sensitive and respectful of the community they're in. And if a Noahide doesn't want to follow the customs, he should not involve himself in the community.
Monogamy and other issues of such scale would be case-by-case, I'm sure, with the community. Noahides don't have a common practice of polygamy, and I doubt one who did would be accepted into a community by such a rabbi as you mentioned, so it would not be an issue.