For the most part, I gather that an Ashkenazi should not follow Sephardi minhag or vice versa. (E.g. - nusach hatefilla, kitniyot on Pesach.)
I am Ashkenazi. I am somewhat "liberal" regarding my use of shechita, i.e., I will use meat that is certified by a reliable rav. I am unfamiliar with what makes "Bet Yosef" shechita, generally use by Sephardim different from Ashkenazi shechita. Would an Ashkenazi be allowed to use Bet Yosef Shechita or can a Sephardi use a reliable Ashkenazi shechita or are they restricted to Bet Yosef shechita?