A sensible person wouldn't say such a thing.

Literal

Discernment [possessive-のある] person [if-なら] such thing [topic-は] say-not would.

分別のある人 means 'a person with good judgment.' ~なら sets up a hypothetical: 'if we're talking about a sensible person...' ~ないだろう is a soft negative prediction: 'probably wouldn't.'