The Muslim migration to Europe in recent times has caused social tensions in at least two ways.
First, there are tensions between Muslims and the ethnic groups native to the European countries. There are problems, for example, with Turkish Muslims being kept separate from German society even though many of them have been born in Germany and lived there all their lives. There are also issues with how much to force the Muslims to integrate with the dominant society. This can be seen in particular in France with its recent ban on full-face veils.
Second, there is tension between anti-immigrant and more liberal factions within the ethnically European communities. This can be seen most horribly in the recent massacre in Norway that was committed by a fanatic anti-Muslim against white Norwegians. He saw them as the enemy because their political party is more pro-immigrant.