I doubt if any state labor laws would cover anything like this other than to outlaw it.

If you are salaried, maybe they could enforce it, but if paid by the hour, I would suggest they have no control over you outside of working hours.

However, if you upset them they can make your life difficult or even sack you, which would be very bad in the current financial situation.

I was in the British military and we had the same rules as the US military but there were still times when everyone came together socially, like christmas parties when everybody in a particular work area or platoon would go to the pub together with no problems. And if you went to a class or a sailing club or something like that, the fact that soldiers of other ranks were also there would not make it ilegal for you to join.

It seems strange in "the land of the free" that someone can remove your freedom to socialize with whoever you like. But at the present time you may be better off just putting up with it.