From the author's README on Thunderstore

MLB Team Fitteds (Backwards)

Fitted caps for every active MLB team, plus classic teams like the Montreal Expos and Brooklyn Dodgers.

Install

Install with a Thunderstore mod manager, or copy this folder into your ReSkate Mods folder.

Install Backwards MLB Team Fitteds

You need ReSkate and your own copy of skate. on Steam.

Open ReSkateLauncher.exe and go to MODS.
Search for Backwards MLB Team Fitteds and click install. The launcher also installs anything it depends on.
Press PLAY. In game, the MODS tab of the ReSkate menu (Insert) turns it on and off.

Or install it by hand: download the .zip and drop it on the launcher window, or unzip it into its own folder in Mods\ beside Skate.exe.

Maps show up in the ReSkate menu's level list. To join a server running a custom map, you need the same map installed. If the game won't load after installing, see known issues.

skatemods doesn't host or review this mod. The download comes straight from Thunderstore. Only install mods you trust, because scripts can run code.