First we should decide if we are talking about immigrants or born citizens. In the first case, the onus is on the immigrant to conform but, for born citizens, especially later generations, the debate changes drastically.
The question then becomes whether some citizens have a right to change the 'predominant culture'. Was it acceptable for pro-choice citizens to lobby for abortion rights? How about prayer in school (for or against)? Or use of certain religious texts in court rooms? In all these cases, the proponents of change were going against the 'dominant culture'. We don't hear much about it, but many of the challenges to overt Christian symbolism in the US/Canada come from Jewish plaintiffs.
What makes these citizens more equal than the Muslim ones?