I would note that, at least here in the US, if our military personnel are wearing their dress uniform for any reason (solemn or not), they are typically wearing their medals or a representation of them (here in the US, we use a ribbon, colloquially known as "lettuce", on a ribbon board on the left chest). Period. That being said, if you earned it, wearing it whenever you want would be perfectly appropriate, no context required. Example being a bronze star. If you earned it, wear it. Put it on your board shorts if you want.
If that's the official rules that it's OK to mow the lawn with your purple heart and bronze star, who am I to argue
I would explain that my reasoning for not doing so is more conservative, in that if you aren't sure if something would be offensive or disrespectful, then don't do it.
Personally, as I don't wear my karate uniform outside of the dojo, as a matter of respect to the uniform and the dojo. So it's a matter of the wearer disrespecting the medal and all those who earned it (not just the medal recipient in question) that is on the line. So I wouldn't advise mowing your lawn with your bronze medal. Nor would I advise wearing your steam punk costume with your bronze medal (barring some really special situation like a band of former military/steampunk friends doing a military send off for a friend).
