This is quite a grammatical question, and i know in Korean 'a, the, an' don't exist, instead using counters like 개, 마리, 권 etc. In English a countable noun is a noun which can be counted;
e.g I had A cup of coffee = i drank one coffee
He ate AN apple for lunch = He only ate one apple for lunch.
A and AN are used as counters to indicate = 1 thing, object, idea, concept etc.
However, sometimes, a noun can be counted even without A and An, it depends on the context:
e.g The man voiced his opinion = The man said what what on his mind, BUT it states 'opinion' NOT 'opinions' so that indicates that the man only has 1 opinion. SO this is still countable.
Uncountable nouns, are nouns which simply either can't be PLURAL or need a 'counter' in order to be made plural:
"I want A milk" = is incorrect, since milk cannot be counted = milks, also is not a word. We have to say "I want A BOTTLE of milk" This is no different to 권, 개, 마리 etc.
news = newses? = is not a word, uncountable = a PIECE of news, SEVERAL PIECES of news
Furniture = a furniture? = in correct, uncountable = A PIECE of furniture
This is tricky because, there are so many words that are countable or uncountable, and the only way to learn them is when you find them.
As for "I had negative prejudice about classical movies" = "Prejudice" can be counted = "I have A prejudice against people who fart in class" = I have only 1 prejudice.
"He holds MANY prejudices against his people" = He has A LOT of things that he dislikes about his people
"I have A negative prejudice against classical movies" would be grammatically perfect!
I hope this is okay? If not, i can re-write in Korean (with lots of mistakes :)