- That's stupid
It's clearly talking about the idea. No one says "That's X" when referring to someone. When someone shows me a painting and I say "That's beautiful", I'm obviously referring to the painting, right?
Similarly, if you come up with an idea and someone tells you it's stupid, you might conclude (especially if it's a recurring pattern) that they don't think you are very smart. If that is not the conclusion they wanted you to come to, it is on them for not communicating better
Saying that a particular painting is bad does not imply that everything that person has painted is bad.
No, but I think the choice of adjective is important. Suppose instead of saying "That's a beautiful painting" I said "That's a masterful painting".
The sentence structure is the same. The adjective is still modifying "painting". I'm still saying the painting is good. But the word I chose more directly implies a judgement of the artist: I am describing the painting as the product of a master painter.
I get the same impression from hearing "stupid idea". Stupid is a description of intelligence, thinking ability, aptitude: attributes which lie with the idea's originator, not with the idea itself.