I learned that "anybody followed by negation" (e.g., "Anybody did not go there.") is grammatically wrong, and we should say, "Nobody went there," if we want to say that the place was not visited by anyone.Is it wrong to say, "Any guy who has common sense should not talk like that."?
Should I say, "No guy who has common sense should talk like that."?
Your sample has a "who" in it, and that changes the picture.
No one had common sense. .
Not *Anyone didn't have common sense.
No one with common sense would say that.
Anyone with common sense wouldn't say that. -- Same meaning
Anyone without common sense would say that. -- This is grammatical, but not the same meaning. It's unlikely.
I'm not a teacher, but I write for a living. Please don't ask me about 2nd conditionals, but I'm a safe bet for what reads well in (American) English.