The Muslims, as the Ummah, care only about proselytism (da'wah), that is, to convince us that Islam indeed is the One True Religion, and thus make sure we "revert" to it, so the world eventually will become Islamic. I see Islam as probably the oldest and most powerful globalist movement, whose goal is to exterminate the very concept of "nations," "state," and "land;" the whole world will be only one nation, the Nation of Muhammad - al-Ummat al-Muhammad. For this reason, serious Muslims are anti-Nationalists (which is a good thing, but doesn't necessarily make bad people into good people). And this is the whole reason multiculturalism is an issue at all today. Naive politicians preach about cultural multitude and cultural relativism because they want to make sure no one think they are racists. The problem with though is that when we "respect" other cultures for mutilating the genitalia of women ("female circumcision"), we are actually insulting them, because we allow them to live like savages by not helping them to progress.
TL;DR: No, the serious Muslims don't care, as long as they can say "Allahu akbar!" and marry away their nine-year old daughters to 50-year old men.
You mentioned neo-Nazis, which reminds me about what I'm being told by "the white, Nordic man" due to my anti-Islamic opinions; because I tell people how Islam really is - and I should know, living amongst zindiq Shi'ites and reading about my fatherland's history constantly - I'm accused of "Islamophobia" and hate speech. I use quotation marks on "'Islamophobia'" because I see this word as a means to scare Islam-critical, or in my case anti-Islamic, people from telling their opinions about ultraconservative, destructive religion, pretty much like when zealot pro-Israeli people accuse anyone who in some way criticises Israel for being an anti-Semite (the problem with this word is that it doesn't just mean hatred against Jews, but Arabs too, because they're a Semitic people too). I'm personally pro-Israel, but it's ridiculous to call any Israel-critical person an anti-Semite. Anyway, what I was going to say before I got off-topic is that had I also been a "white, Nordic man," I would be accused of racism because like we all know, Islam is a race... the fact that I'm a Sweden Democrat doesn't make things easier for neither: "how can you vote for them!? They're neo-Nazis!!! They hate people like you!" They're only called neo-Nazis because the media here is totally distorted by leftism.
