I'm seeing the issue in slut mode. After you find your clothes on the ground, it will put them back on the sprite, but not equip the jacket in your items. I tried this while wearing nothing before finding the clothes, and the bunny suit, and in both cases it won't equip the jacket.
Viewing post in Bug Reports Thread - Version (0.5.1 to 0.6.2 (Content Pack 1))
Ahh, ok, that makes more sense. Still having trouble reproducing though: once I've picked up the clothes again, the jacket is equipped in the armor slot for me. Any chance you have a save from just before picking it up that will demonstrate it happening? All the clothes pick-up locations are referencing the same one chunk of code, so they should all work the same. Not to be annoying, but are you sure you're checking equips and not items?
I think I see what my problem might have been. When I downloaded the newest version of the game, I just dropped everything into the existing folder, replacing everything with the newer version (I wasn't sure where the saves were being stored, and didn't want to lose them). I deleted my game and did a clean download and it looks to be working as intended.