Ok I think I have a good example:
Birchos Kohanim. There is a mitzvah for Kohanim to duchan they make a beracha and eveything.
Yet among Ashkenazim the minhag in chutz learets is not to (aside from Yom Tov.
I am guessing based on this minhag the Kohanim in your shul didnt fulfill the mitzvah/halacha of birchos Kohanim today.
Is this a good example?
(Yes I know all the (weak – even according to those who give them)justifications for our minhag. that in no way changes my point)