A couple of points:
1. You will not be considered "weird" for following your beliefs. Folks that would make comments about your decision not to perform circumcisions would only show how shallow themselves are.
2. Even though you don't believe in the procedure, I would still highly recommend watching a few as you may ultimately end up in a situation where that knowledge might become necessary. For example, I don't perform circumcisions since its not within the scope of my practice (MFM), but I do supervise residents on L&D and have on occasion been called for a complication (bleeding) and it does help to know 1) how its done and 2) how to manage complications. Not to draw a literal comparison, but for example if you were to not perform abortions, it would be wise to at least know the associated complications and how to manage them.
Congrats on starting residency. Best of luck!