The Vilna Gaon said that we should not decorate our Shuls with greenery on Shavuos even though the Rema paskened in Shulchan Aruch (OC 494:3) that we should. The reason he says is because the non-Jews have “stolen” this minhag and we don’t want to be like them. Many argue that since we did it first, why should we care what other religions do?
Rav Mordechai Epstein brings proof from a Rashi to the Gra. It says in the Pasuk (Devarim 16:22) that we should not bring a Korban on a Matzeivah, even to Hashem, because Hashem hates it. Rashi says that although the Avos did it and Hashem loved it, now that others have adapted it as part of their service, Hashem despises it. We see from here that even something that was considered a mitzva can become despised once non-Jews take it on for their worship.
From revach.net