The guns – pistols, rifles, or smoothbores – used at living-history events are real, live-firing guns. At least the ones I use are. Re-enactors are firing blanks. As for carrying them or any other gun in public, I would suggest you go by your state's gun carry laws.
If you're talking about non-firing replicas, I would suggest not carrying them in public as others will consider you to be armed with a live-firing weapon, especially the police.