What is the rule on saluting another battalion’s colors while on road guard?

Must be a difference in services on this. In the Army, at least in the 80s-90s, unit colors wre not saluted, only the US flag. In AR 600-25, in the section about rendering salutes to uncased colors, it specifically defined the term colors as referring to the US flag.

On unit runs, etc, if a formation was being led by say a Bn Cdr with his colors along side him, the person leading another unit would salute the officer, not the colors, and the other officer would return the salute.

General Order 10 for Sentries (Emphasis added). I believe in the loosest terms a "Road GUARD" is a Sentry.

To salute ALL officers and all colors and standards not cased.

However, never put life, limb, or sight at risk to render honors (Saying "By your leave" is considered acceptable in Naval tradition).

That said, better safe than sorry. It is the National Ensign.

I have never seen this in the Navy, but if the road guard was engaged in their duty of keeping their fellow soldiers safe, I would think there could be a CSM to CSM talk (as would happen in the navy) to ensure the individual who was offended understands why the soldier did not render honors if required. I think this is an issue where common sense should (loosely) apply...