It's always best to clear with your sponsors. But as a designer, its also (IMO) the responsibility of the team to clear their own sponsors. If you make an original front logo for a team (aka Rocco's liquor depot,) and they want bud light as a free advert on the sleeve, tbh, I don't think twice. And i'm not naive. I know that these brands are aware this happens (not that this justifies any actions of legal wrong-doing.) Conversely, if you're using a brand as the main focus of the identity of a shirt, i'd never feel comfortable with that without OK from someone within the organization. Its a softball uniform, the worst you're going to get is a cease and desist, and since its a one-off production, you've legally complied. They probably aren't going to send people to make sure you don't wear them to your co-ed games. But ethnically, It's one thing to put Tanel on a sleeve because you love the brand, it's another to make a Tanel sweatshirt with whatever crazy (and possibly inappropriate) designs you can think of without their OK. Companies have every right to protect their copyright.
It's just a very slippery slope a designer of a one-off softball jersey that will be seen by, at most, a few thousand people for a few moments.