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There is no prohibition or even any official discouragement from registering under the political party of your choice while on active duty. That said, there is also no particularly compelling reason to register, especially if you intend to register as a Democrat, while on active duty either.
Active duty personnel are prohibited from taking an active (read "campaigning") part in the political process, though this prohibition is not absolute and is enforced to varying degrees.
One reason that one might not want to register as a Democrat while on active duty? How about the preponderance of Republicans that surround you in the military which are part of a party often that uses words like traitor, anti-American and communist/socialist to describe people who are part of other (read "Democratic") parties?
I don't have an issue with Sestak not registering any affiliation in 2006. I do have an issue with the fact that he's yet another Blue Dog Republicrat who would have fit in with the mainstream of the Republican Party in the 1980's. And as for Specter, what was his affiliation in 2006? Yeah...thought so.