Is it disrespectful for a civilian to wear a woodland camo pattern BDU?

I tend to go to thrift shops and find good deals, a complete set of 1980s woodland camo uniform, minus the name tape, branch tape rank, unit and flag patches, and qualification badge being one of those deals with an 8-point cap. Is it disrespectful or illegal to wear the uniform to a Fourth of July parade as a salute to veterans and current service members? Just asking so no one screams “Stolen valor!” or gets the wrong idea. I myself am a civilian and my buddy and I want to join the military.