Where and what service? I live near Ft. Hood, and we see troops, I've personally seen officers as high as Lt. Col., in all the restaurants, all in BDU's.
At one time, long ago and in a galaxy far away, we could not wear fatigues (pre BDU days) off base, but we could wear our "regular" uniforms. Including both the ones with the blouse (jacket to civilians) and the one with a shirt only, with or without tie.
LtCol, USMC.
Yes, there are people on liberty in certain military uniforms. In general, there is no definitive answer because regulations differ among the service branches. The working uniform of the day for pilots is an issued flight suit, and wearing one outside of a vehicle off-base is prohibited. Rules are more lenient while wearing more of a dress-type uniform or alphas and not cammies. We've certainly worn Ball attire to restaurants, etc.
Under no circumstances that I am aware of would any member of the service in any branch be permitted to rally or protest in any official military uniform. Wearing a military uniform and insignia is a privilege given to someone who has earned the right to wear one. And wearing one makes an individual a representative of that branch of the military. The military does not endorse rallys or protests, etc.