You're really muddling your point by phrasing it this way.Being anti-immigration has nothing to do with being racist. You also can't sustain a welfare state while letting everyone in. Neither is islam a 'race' but an anti-democratic, misogynistic, anti-feminist, anti-minority, anti-secular religion that spits on liberalism that you so apologetically approve of.
Religion itself doesn't matters, people following the religion do. What islam says is irrelevant, what matters is how people of certain country decide to follow it. It's perfectly true that a majority of people in poor islamic country agree with statement like "It's okay for a husband to beat his wife", but the key word here is "poor" not "islamic", they'd agree just as much if they were following another religion or even no religious. Poor country make for poor culture which makes for poor people. Muslim that grew up in richer country tend to disagree with the statement, the longer they'd been in the richer country and the richer they are, the more likely they'll disagree.
It's also true that immigration can collapse a welfare system, think what would happen if the entirety of the sub sahara population was teleported to Germany overnight. But some level of immigration are perfectly sustainable and alternative exist. One alternative is to levee higher tax on immigrant until they pay back a certain amount, another is to have a multi tier welfare system. Immigrant don't go to certain country for welfare, they mostly move because their country is a terrible place to live in and they just want to be somewhere where they don't have to worry for their security everyday.