It looks really good. One thing I would recommend is specifying roughly what year (or range of years) you're showing on the map. I know you mention it here that it's roughly post-First Crusade, but since you show the routes for the First through Fourth Crusades, I'd include the time period in the title to avoid confusion.

In general, for your Islamic naming concerns I'd recommend checking out Paul Cobb's The Race for Paradise. His book is an Islamic History of the Crusades, and it's a great resource for all things on that topic. He also has some good maps. For reference, he uses the Seljuks of Rum, rather than the Sultanate of Rum. That's a pretty small change, but does help to clarify that they are part of the Seljuk Turks.

A more important change is that the Almohads should be the Almoravids. The Almohads overthrew the Almoravids around the time of the Second Crusade, so too late for this map to show them. Despite there very similar names, they are actually two distinct dynastic groups, rather than different spellings for the same (like I believed for who knows how long).

The last thing that pops into my head is that it might be worth trying to map Sunni and Shi'a Islam onto the map, rather than just 'Muslims'. Since you've shown divisions in the Christian Church, it seems logical to do the same for Islam, especially since those divisions were integral to the success of the First Crusade. It might be hard to map exactly where majority Sunni vs. majority Shi'a groups lived, but I'd at least think about colouring the Fatimids differently to mark where the ruling dynasty was a different sect.

I would also add Mosul to the map. It's an important regional capital, particularly for the Seljuks, and a useful reference point for people.

I already mentioned The Race for Paradise, but I'd add Peter Frankopan's Call From the East as worth looking at. I recall Frankopan as including some excellent maps of Byzantine territory that might be useful to you.