The Brief: Don't @ me means "don't contact or respond to me."

Bluesquiggle
DEEP DIVE

The phrase is pronounced “don’t ‘at’ me.” The “at”-symbol (@) refers to the tagging of someone’s username, so that they get a notification of the engagement.

On Twitter, users cite this phrase after sharing an unpopular opinion or hot take. The idea here is that their statement will stir up much controversy and discussion, but they do not want to be a part of that dialogue.

https://twitter.com/mike_granado/status/1095334656260468737