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.