Template Used Changes if Logged In?

I’ve got an odd one. A specific category on my site displays using a different template depending on if the user is logged in or not. When logged in, it uses the correct template, but if the user isn’t logged in, it renders using a template from a different theme altogether. The themes aren’t parent/child or anything like that, either. Trying to fix it, I deleted the offending theme, but now the incorrect theme displays without the benefit of a stylesheet. Again, when the user is logged in, the category displays properly. Even after the user logs out, it displays properly. If the user’s cache is deleted, however, it goes back to displaying using the wrong template. Has anyone else run into this behavior?