There's already language in NFL contracts that speak to what you're saying..
Yes, there are some things pro athletes aren’t allowed to do
But like the article itself states that's a very vague bit of wording and doesn't really do much to specifically tell any particular player what is actually allowed and what isn't. As the article also further points out there are particular players that have much more specific language making certain activities prohibitive. Which is why I brought up a few examples of what you think should be prohibited.
As well it says that there are also contract stipulation that allows for frowned upon activities, but at financial risk/liability to the player.
It's clearly between the club and the player what the do's and don'ts are when the dotted line is signed, but I think it's important to make those lines clearly drawn without just broadly saying 'hey, you can do stuff in your free time if you might get hurt'.