Is it illegal for a civilian to wear any part of the ACUs (as I don't fall under AR670-1, but I do fall under the 1st amendment)?

Only if you are wearing the entire uniform or parts of it to gain some sort of favor or personal gain. I never served in the Army or Marine Corps, but I have ACU pants and MARPat pants that I wear on the range and while in training.

As a Veteran I wear my uniform on Memorial and Veterans Day. As for civilians, some are going to do it regardless. Besides, there's no AR670-1 Police in every country and state to check EVERY person that has a piece on.
Stolen Valor will continue to happen. Some people have a real ignorant view of military; especially when they've never served and don't know the basic things about it. The people who do it don't care either. I can only hope some Active Duty and Veterans put them in their place.

No it's not illegal.

I see many people wearing different parts and it does not become a problem unless wearing it as a civilian and trying to pass yourself off as military. If you can but this clothing at anyplace other then a military base then it is fine to wear.