Not the asshole. You shouldn’t worry about looking up someone’s reddit acct, it’s a public forum, it’s out there. The “husband” thing is whatever, maybe it suggests they see each as other as being married, even if not officially so, just a theory. Reading everything else you put here though would make me suspect that there’s more going on between them than what she lets on. That she deleted the post is interesting.

However, since you’ve described your relationship as just casual dating, I’m not sure that she’s in the wrong in any way either. If you want it to develop into something more you should probably establish boundaries or at least communicate to her that’s what you want (if you haven’t already done so). It sucks to act like a jealous lover, but if you’re not comfortable having somebody else in the picture, people need to make choices about who they’re spending their time with. If she doesn’t want to take it further, then it’s just casual and you should probably accept that it may not ever develop past that or that you may not be a priority for her. If you want more, you’d likely need to start looking elsewhere.