As a followup to the thing I went through: I did confront my coworker. I spent a few weeks feeling like I couldn't bring it up because it's so small. This particular lady had always treated me funny so I didn't expect the conversation to go well. She said this was how they did it at her house (separating mugs) and I shouldn't care about it. I was the only dude on the staff so it just felt like I was being isolated from the group with mugs! I felt immature for even bringing it up. She stopped doing it for a while but when she switched shifts I'd get in the next day and see she'd done it again... it still makes me irrationally angry.
Now I just don't drink coffee, haha. XD