I think it would be a tough road for them if they sought civil remedies. As best I can remember (I don't have time to research the issue now), the federal courts have been fairly deferential to the armed forces in these types of cases, even after the Lawrence decision regarding privacy. I think that only the 9th Circuit (obviously) has held the armed forces to something higher than the "rational basis" standard in these matters.
ETA: In other words, they're going to have to prove a heck of a lot to make their claim stand up in court.
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