Sucks to be going through such a thing. I take it you don't have a union rep to help you?
It would seem extremely excessive to be fired over such an account.
A colleague I worked with in my previous work place, came out with a line along the lines of "Nice tits! They'd look even nicer with my cock between them/ my cum on them" (one or the other) to a female colleague on a works night out, at his previous workplace.
Unsurprisingly HR were informed, and I think he was outright fired for that, IIRC.
And then when he was in the same workplace as me, when he was presenting one of his regular update meetings with his clients, and they were not pleased that he didn't have certain information that they wanted, he responded "What do you expect me to do? Pull the figures out of my arse!?"
Unsurprisingly that client group immediately left our business, and that guy was fired very soon afterwards.
It doesn't sound like you've done or said anything anywhere near as inappropriate, and more importantly, to the wrong people, so it would seem a gross over-reaction to get fired over what you've said happened.
I hope your appeal goes well.
Are there any other managers, or senior, well respected colleagues. or HR people who you get on particularly well with, and could go into your appeal with you, and help you present your side to best advantage? Not that I don't think you're capable of doing that, but I would imagine it would help you to get someone like that on your side.
That's if you'd want to keep working there anyway after all this. It mightn't be easy for either party to forgive and forget, and move on, if you end up keeping your job, and possibly getting some kind of warning only.