Which culture wins?

In Austria, an Austrian man is fined for yodeling, as it offends his Muslim neighbor:

Austria: Judge Rules That Yodeling Offends Muslims – Politics & Gov’t – Israel News – Israel National News.

This raises a question: when two cultures come together, how do they begin to integrate?  I mean, on the myriad differences between them, who determines which culture wins, and how is that determination made?

I would suggest that the majority culture should hold sway.  If I’m living in Austria, with a rich tradition of yodeling, perhaps I should modulate my thinking to accept yodeling.  It seems quite rude to move into someone’s home and demand they cease centuries old traditions to protect my sensibilities.