The question :)
Bonus points if the word implies that they try not to antagonize anybody. It's like a guy betting on the horse that's winning, but keeping his options open about changing his bet
I'd say fickle works quite well here, but you would need to make sure the exact meaning can be ascertained from context.
Marked by lack of steadfastness, constancy, or stability : given to erratic changeableness Source: Merriam- Webster
In my experience, fickle is usually used to describe someone who "backs the winning horse".
He supported England last week, but now Wales are at the top of the word rankings, he'd claiming to support them. He's so fickle!
For your "bonus", I would suggest the phrase:
Hedge your bets - to protect yourself against loss by supporting more than one possible result or both sides in a competition Source: Cambrudge Dictionary
Or, that he doesn't want to:
Put all his eggs in one basket - If someone puts all their eggs in one basket, they put all their effort or resources into doing one thing so that, if it fails, they have no alternatives left. Source: Collins Dictionary