This is exactly the kind of thought terminating cliché that makes people despise the Left and vote Trump. Of course Muslims are people. So are Buddhists, murderers, mothers, Nazis, and so on. In fact, literally all people are people. A kindergartner can tell you as much, so how is this anything other than dismissive, empty rhetoric?
The real issue is obviously not their humanity, but their beliefs. It makes total sense to see them foremost as Muslims given the importance of Islam to their identity. Acknowledging this doesn't mean you're dehumanizing these people, it simply means that you're not willfully blind to the fact that beliefs substantially influence how people behave.
The real questions that should be asked and addressed revolve around the compatibility of that identity with the US society. Do US citizens like living among Muslims (i.e. people that are culturally quite distant from themselves)? Does it introduce ideological and social friction? Does it enhance society or not?
Those are the questions that the liberal Left doesn't even attempt to answer, because they're completely fixated on abstract moral dogmas (-isms like racism, sexism), which coincidentally is a privilege often afforded by not having to suffer the actual social consequences of those dogmas.
When you don't apply the same "people" standard to Muslim and Christians, when you want to strip one of those classes from free speech, from free entry into their country or their religious freedom, do not be surprised if "the left" ( but really, anyone) gathers that they are not being seen as people.
The reasonable questions you are asking are not the questions your (I'm assuming) party is asking. The answers to those questions are also extremely different to the answers that same party is coming up with. You don't solve a cultural difference problem by removing the culturally different, that's just making it worse.
How do you define muslim? Is it someone going from muslim country who is not religious? Someone who goes to mosque once a week? Or someone who is praying all the time and tries to convert other people to his believes? Are all those groups really causing problems for you or society?
A Muslim is a follower and believer of Islam. A non-Muslim from a Muslim country is not a Muslim, while a Muslim is. I really don't get why you're asking this. I assume the answer would be obvious if we were talking about Christianity or libertarianism or any other distinct set of beliefs: if you believe in them, you are a believer.
Whether any belief system has the potential to cause problems for a society depends on the content of that belief system and the content of the belief systems already present in that society. In the case of Islam in particular, there are two facts worth noting:
First, a strong case can be made for major compatibility problems of mainstream Sunni Islam (MAI) with Western societies. I won't go into details here, but very generally speaking, MAI has a theocratic component: Muslims should, in theory, strive towards the implementation of sharia law. As a body of laws and in terms of its axioms, sharia is simply incompatible with the Western legal tradition. I'm sure that what I'm saying here is not controversial among MAI Muslims. Your average Muslim (assuming he's honest) will corroborate this.
Second, Muslims come from a culture that is very unlike that of the US. Even if there were no incompatibilities, the bare fact that they're so culturally distant poses a barrier to the formation of the social bonds that are necessary for high trust, high cohesion communities and societies. In case that's not obvious: people generally bond more with others with whom they share the same cultural reference frame and state of mind.
Supposing you grant me these two arguments, then the potential for causing problems for a society is established. Whether that potential is actualized depends on the demographic weight a group has and the extent to which it is willing to compromise.
Speaking as a Dutchman (and realizing that the demographics of our Muslim population differ substantial from that of the US), it is clear to me that Muslims as a group cause problems in both senses. For example, in areas where there is a substantial Muslim demographic, there are now local political parties that explicitly cater to them. We never asked for this and we don't want it, but now we're stuck having to deal with it and with the social friction that comes with it. Another example: schools with substantial numbers of Muslim pupils are subject to great social pressures by this group, with some not being able to discuss certain topics anymore (Holocaust, criticism of Islam, cheering Muslim pupils during the aftermath of the Charlie Hebdo shootings) and concessions being made at the cost of native students such as defaulting to halal food. If you want sources for any of these claims, let me know.
> I assume the answer would be obvious if we were talking about Christianity
Not at all. Would you stay Christians want creationism to be taught in schools and not evolution? Would you say Christians are anti-abortion and anti Gay marriage?
Sociology isn't maths. Social groups almost always have some internal diversity. That doesn't mean they aren't meaningful categories. Christianity shares a common core of beliefs. It has a common narrative. It has a large set of overlapping beliefs. The same goes for Muslims (and Buddhists, libertarians, you get it).
There are sweet apples, sour apples and everything in between. That doesn't mean it would make sense to start pondering on which of those really are apples, nor whether you should try to sell them in a neighborhood known not to like apples.
Sure, you can subset Muslims into different groups and branches, and some of those will be more compatible with Western society than others. The net impact with zero filtering however is negative.
I completely see the point of wanting to maintain and evolve the current set of social norms, rules and values in a society, and wanting immigrants to integrate well. But I do think that 'Muslim' as a category is too broad, not useful and in fact detrimental to smooth integration where it is possible.
You might as well use a different broad category - say 'foreigner' and whatever you say (erosion of society's values etc.) would hold true in general. Then you could draw the conclusion that foreigners are causing the social disruption and so any immigration is to be resisted.
Basically what I'm saying is, if you point to specific values that you respect and that are being eroded (e.g. 'I dont like immigrants that dont support womens rights') it may be better received than if you transfer the blame to a generic broad category, specially along religion or race, because then you might appear to be a racist.
I think it's about 400 years late to be asking if Muslims are a good fit for US society. Some estimates put the first Muslim in America on the Mayflower, others say 17th century slavery. Either way, Muslims have been in America for a long, long time.