Difference is, in a video-game you're not likely to have people thinking you could be trying to pretend you're someone you aren't
That's why I say best to just leave it, saves any upsets or disputes, some people work very hard for various things and care about who wears them and who doesn't. I know a lot of people from 7th Para- a couple who I asked about the subject just after the last time this topic came up, 1 said they'd not be bothered but advised against wearing it for the benefit of those who would be and the other said they'd not be hugely happy with it, though wouldn't make a big fuss. I imagine some others would be less impressed than that too.
Best just play it safe.