This question is inspired by recent news of events in Beit Shemesh.
What happens halachically when 2 customs collide and each custom affects the other side? In the case of modesty, for example, requiring one side to dress more modestly may be a physical burden on that community. Maintaining their present dress may spiritually affect the other community.
There are many opinions flying around about the present situation but I have heard little about the way such disputes should be handled or were handled historically. I am looking for halachic sources and precedents only, but can be from any matter not just modesty.