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.
That's for sure and for certain.
I guess I'm not surprised that the Marines have stuck closer to the "old ways". Army and Air Force allow wear of BDU's and flight suits in restaurants, gas stations and convenience stores, etc. Their rule is one of appropriateness. You shouldn't wear BDU's to a place where everyone else wears coats and ties, but you might do so where many where "business casual" attire, and there's no problem at all wearing them where civilians are wearing shorts, t-shirts and flip flops, and even the staff is wearing jeans and T-shirts.