There are certain things which may be accepted as proper worship in a religion, but others may consider it Bid'ah.
For example, some people say that reciting "Ameen" after the Fatihah in prayer is a Bid'ah because it is a non-Arabic word. Or that celebrating the Prophet Muhammad's birthday is Bid'ah. Or even specific prayers and acts of over-worship.
What is the proper approach when you believe something is Bid'ah but the people around you don't? Is it permissible to do a prayer that you believe is Bid'ah just to please the people around you, if there is a weak hadith/fatwa supporting it? Is it considered haraam because you'd be strengthening a false belief?
I specifically mean the ones that are relatively harmless, not the ones that lead on to shirk.