A sensible person wouldn't say such a thing in public.
Literal
Discernment [possessive-のある] person [if-なら], in-public such thing [topic-は] say-not would.
人前で (in front of people, in public) uses で to mark the location of the action. The conditional ~なら sets up a hypothetical: 'if we're talking about a sensible person...' ~ないだろう gives a soft negative prediction.