The short and simple explanation of Blair's commodore rank is as capi3101 said above - he moved to the Navy for the Midway project.
The deeper and far more challenging issue just beneath the surface, though, is that Blair and others moved back and forth between Space Force and Navy ranks on a couple of occasions - in particular, the movie has all the pilots with Navy ranks. Afterwards, IIRC, the KSaga version of the WC2 manual has Blair in a Navy rank again. My impression is that this is something that caused a bit of debate at Origin, and never really got anywhere. Presumably, when they were first making WC1, they either overlooked, or chose to ignore the fact that normally, carrier pilots are Navy. But then WC2 references to Blair as a Navy officer in spite of having a Space Force rank, WC3 makes it clear that yes, there are separate Navy and Space Force ranks, and yes, Blair has a Space Force rank (which presumably would mean he is in the Space Force), but then Kilrathi Saga comes along and for no particular reason Navalises Blair's rank in the manual. WC4 just plain ignored the issue (or did it? I don't recall if the "middle" ending has Blair referred to as a general or an admiral?), and then WCP officially made Blair into a commodore, and officially explained in the strategy guide that yes, this meant him moving from Space Force to Navy. Oh, and yes, then the movie came along and said that as a matter of fact, Blair was a Navy pilot - the movie having the freedom to reinvent things that they felt needed reinventing (which caused no controversy whatsoever

).
I suppose one way of looking at it would be to consider the Space Force as a sub-division of the Navy, which gets its own distinct ranks and such. But that doesn't actually explain any of the back-and-forth between one type of rank to the other.
I should add, it would be very unusual, but not absolutely unheard of, for the Space Force to be operating squadrons onboard Navy ships. This was, for instance, the German plan for their own carrier(s) in WWII - Kriegsmarine crews, Luftwaffe pilots. But then again, maybe that's one reason why the Germans never got anywhere with that

.