I.E., if you were asked “You don’t like plastic?”, you could colloquially say that you didn’t by either saying “yes” or “no” (“Yes, I don’t like plastic”, “No, I don’t like plastic”). Is one answer more grammatically correct than the other?
I would look at it as a statement of fact as opposed to a question. I would answer “yes”, as in “yes, that’s true, I do not like plastic.”
I don’t think there’s a concrete protocol, at least in English. For clarity, it’s probably best to reply, “I don’t like plastic.” without a yes or no.
Personally, in the spirit of my ancestors, I’d throw a question right back: “Why shouldn’t I not like plastic?”
Usually for something like this, answering “No” is usually taken as negative, and “Yes” means you’re contradicting the speaker.
Thus the exchange:
“You don’t like plastic?”
“No”
Would indicate you don’t like plastic.
If you contradicted, you’d say “Yes,” but probably would add “I do” to make it clear.
It’s not entirely logical, but then, there’s no reason that language has to be logical. There are just constructions that are understood in a way that doesn’t necessarily make logical sense, and that song ain’t so very far from wrong.
Reminds me of the question, ‘do you still beat your wife?’
I actually encountered this during a test.
Test proctor said all questions had to be marked yes or no. Leave no unanswered question.
Always wondered what the hell they were looking for. 
“Do you still beat your wife?”
“Mu.”
(Japanese Buddhist term meaning, “Your question cannot be answered because it is based on false assumptions.” Handy term to keep in your back pocket.)
Yes, we have no bananas today!
::does Carmen Miranda thing::
There is not a concrete protocol or you wouldn’t have to ask this question.
For clarity, avoid answering yes or no. One has to “correct, I do not like plastic” or “actually I do like plastic”.
It’s like driving and asking directions, “I should turn leftt at the next intersection?”
and the correct answer would be “right”, now wtf does that mean? Turn left or right - it depends on your cultural context/frame of reference, and certainly there is no where close to a universal view.
I think tone of voice has a lot to do with your answer being interpreted correctly. “No” (you’re correct) sounds a lot diferent to “No” (you’re wrong). In most situations it is quite clear and a longer clarifying sentance isn’t necessary. Same when using the “yes” answer.
The fact that the answer to a negative question could be ambiguous is very helpful, for example, in Japan. It is considered rude in Japan to answer “No.” So, if you ask a yes/no question of someone, they will almost always answer “Yes.” (Truth is not absolute, and truth is not as important as good manners and harmony.)
Hence, to get an honest answer, you ask the question negatively.
Example: “Will it be convenient for you to meet at 2 PM?” answer will be “Yes”, regardless of reality. (The assumption is that you set the 2 PM time because it was convenient for you, and it would be rude to suggest a different time.)
However: “Won’t it be convenient for you to meet at 2 PM” will allow the answer “Yes, it will be convenient” or “Yes, it won’t be convenient.”