Yes, there is a continuum. I have met many muslims both in real life and online that are outright hateful and closed minded, and I have met ones both in real life and online that are pretty fairminded and borderline liberal, and I have seen them fight about this amongst themselves.
The core problem with Islam is that it is literally the "surender of oneself as a slave to Allah". It is based on obedience to power, even more so than Christianity is, so it operates even more so on tribal lines of ingroup and outgroup. I can't see any way to change that, as it is baked right into the core of the religion. And even the peaceful "moderate" muslims have this problem. They are just as blindly obedient to Allah. They just differ on what Allah wants, and that seems rather arbitrary to me.