It’s hardly rude, let alone “extremely” rude. People who are transgender are straight up told to kill themselves daily on social media by bigots and you’re melting down over someone having the temerity to question some random account’s (ie, you) credentials? Grow some thicker skin.
It's definitely rude to suggest someone is lying.
You think telling someone to stop being rude and then not continuing to engage with them is melting down?