Is the word "beans" as in red beans a countable noun or an uncountable noun?
It's countable, since the singular is "bean."
It's a bit of a mystery why "bean" is countable and "rice" isn't. Most countable nouns are for things that can be gotten by the individual unit, and non-countable nouns tend to be commodities that are gotten by the pound or the cup or the pint. "Cow" and "pig" are countable, while "beef" and "pork" are not. For what they are used for, beans and rice are just similar enough that they should be treated the same in the language.
It's significant that "bean" is of Germanic origin, while "rice" is from Italian and French, both Romance languages. When foreign words come into the English language, they tend to keep their old language's spelling and rules, and I would guess that this is why "bean" is countable, even though it's likely impossible to go out and buy one single bean.