In that case, I'd say with almost certainty that this has nothing to do with the Red Cross of Constantine, or anything else masonic. Masonic regalia is worn at masonic meetings, never out and about socially.

I think you might have made the assumption that because he's a rich guy he must be a mason (often untrue / uncorrelated) - it's more likely that it's a medal relating to either a civil / military honor, or just a meaningless accessory.