My truck has its original markings, including "US ARMY CU0222 Official Use Only", "MS-TMP-06", etc. The First Amendment protects my right to paint anything I like on my truck. There are limits, but those limits don't involve anything that interests me. I see this as me preserving a small piece of our history, and I intend to keep it as accurate as I can.
DoD regulations apply to Service Members and the people who live and work on DoD facilities, not to non-DoD civilians. We civilians have to obey laws against Stolen Valor, Impersonating an Official, etc. None of that applies here. We have to obey DoD rules on DoD facilities, but that's mostly about traffic rules and proper vehicle paperwork.
No one with a clue will look at a truck with civilian plates and think it's an active military vehicle. No one with a clue will look at an out-of-shape old graybeard like me and think I'm trying to impersonate anyone, with the possible exception of Santa Claus.
It is certainly possible for us to offend people. I wince a little every time someone refers to this group as SS. But common sense and common courtesy should satisfy anyone with the slightest clue.
Idiots like the Parade Organizer who berated the OP, well, they exist, and there is no known cure. When someone gets in my face like that, I find myself struggling not to laugh, which seems to only further infuriate them. I coach my kids to deescalate and disengage. Failing that, ask to speak to a supervisor. There's no point in allowing a tantrum to escalate into a physical confrontation.
For the OP, I think a letter to the organization is definitely in order. It's the veterans that would lose out when stupidity like this prevails, and I *really* make an effort to make sure they don't lose out. But sometimes, stupid wins. Especially in politics.