Not that, specifically, though it might be indirectly?

I'm basing it off of one of Gyles Brandreth's yarns where he described how he dealt with abusive constituents when he was a MP.

Dear sir or madam:

Some crackpot has written me an abusive letter, and they've signed your name at the bottom. [...]

Whether he came up with that or adapted it from something prior, I don't know.

Sadam.

I'd guess "To whom it may concern" would be the most gender neutral/inclusive way to rephrase that.

"Dearest snookums"

Not that I know of. Unless someone has stated their gender or pronouns, I just use people's names and avoid anything that assumes or implies gender.

"Sir or Madam" already is a "They/Them".