Just curious.
Depends on what service operates them, and/or what service that service is descended from. If this authoritative source is to be believed, it’s probably going to be Air Force. 
The Air Force has had the most direct role in space type design and operations. The Air Force makes the most sense and I can’t see it following Navy convention unless they make a convincing case that a certain space vehicle is just like being in a nuclear sub.
If by the time we allowed ourselves to militarized space happened the ships would most likely be huge and the missions extermly long. They may then go with Navel type rankings. A navy captain commands a large vessel and out ranks an Air Force captain who merely pilots a realitivly small plane.
Then again why not have all the services represented. Navy commanders for the mother ships, Air Force captains for the small fighter vessels, marines on ship for small tactical strikes requiring manpower, army ranks for the clone army and knighthood for the Jedis.
For all we know NASA might be absorbed into the US government to become another branch of the military. It will all depend on the politics surrounding the decision.
My money is on the Coast Guard.
Ah, so they’ll be using Navy ranks. Cool. 
Wouldn’t it be analogous to aircraft? Aircraft are operated by all of the various military services and the crews ranks reflect that of the service they belong to. Presumably spaceships would be used by all of the services as well.
I participated in the Columbia Shuttle Recovery in 2003. I cannot offer a cite to verify this claim, but we were told that every Shuttle mission was/is a military flight, and every Shuttle is (technically) a military aircraft.
The Air Force already has a Space Command. Nowadays they just drive satellites but they’d be the lead in any manned military space vehicles that might be on a drawing board somewhere.
I seriously doubt this is the case. Granted, some astronauts are military officers but that doesn’t mean the mission itself is a military mission.
I’m not sure how it works, but it appears you are right. I used to have a fascinating book in the form of a thick magazine that provided all sorts of information about Air Force planes and spacecraft, and the STS–“Space Transport System”–was listed as just another category of aircraft with the description of how it was used. However, I also remember reading that the the Shuttle was no longer being used to launch military satellites, and I’ve also read that nowadays most astronauts are civilians. So how it’s all sorted out in terms of jurisdiction I don’t know.
A Navy Captain is an O6 paygrade I think. The equivalent Air Force rank would be a Colonel.
An Air Force Captain is an O3 paygrade. The equivalent Navy rank would be a Lieutenant.
Why wouldn’t the US just add another branch, much like they did with the Air Force?
The Air Force evolved from the Army Air Corps after WWII, this they have a very Army like rank scale.
I say we think outside the box and use RAF ranks 
… Leading Spacecrewmen, Flight Lieutenants(OK, so we’d probably pronounce it Lootenants), Space Vice Marshals, anyone?
Yeah, Wing Commanders would be good!
You’re all wrong. We’ll be using the ranking system from Battlestar Galactica.
NASA is an executive branch agency, and was thus from its beginning fully part of the U.S. government. My knowledge of NASA history is poor, but I seem to recall that there was a struggle within the Eisenhower administration to keep NASA civilian, contrary to the recommendations of the DOD. This is not to say that NASA is entirely separate from the military, since, as has been pointed out, many (probably most) astronauts were/are members of the armed forces. In addition, there have been several Space Shuttle flights with classified military payloads, e.g., STS-27, although I agree that given NASA’s status as a civilian agency, any of its craft proper (not counting the delivery system, such as a military rocket) are probably not considered military craft. The closest the U.S. military has gotten to having a long-term presence is space is the failed Manned Orbiting Laboratory program of the late 1960s.
As for the OP, I suspect that given the USAF’s long history of participation in space flight (having beat out the Army and, to a lesser extent, the Navy for primacy in the late 1950s/early 1960s) it would probably continue to provide the model were the U.S. to develop military spacecraft.
Yeah, well this authoritative source says Navy.
Seriously, it seems to me that the main thing that the Air Force and Space Force have in common is that they are above the earth’s surface. But the Navy and Space Force share more relevant things, like the size of the vehicle and the command structure of the personnel.