Is "dirty money" a noun or a noun phrase?

According to Cambridge, M-W, and Vocabulary.com, dirty money is classified as a noun.

Entries of noun from Cambridge:

a word that refers to a person, place, thing, event, substance, or quality

and from M-W:

A noun is usually a single word, but not always: cake, school bus, and time and a half are all nouns.

An entry of noun phrase from Grammar Monster:

A noun phrase is a group of two or more words headed by a noun that includes modifiers.

In "dirty money", dirty is the modifier. Why do they say "dirty money" is a noun rather than a noun phrase?

It depends on how the phrase is being used.

If you're talking about currency that literally has dirt on it, "dirty" is an adjective that modifies the head noun "money", so it's a noun phrase.

But "dirty money" is also an idiom that refers to money that was earned from illegal or immoral activity. If this is what you mean, it's a compound noun like the "school bus" example. This is the meaning in the dictionary entries you linked to.

The second sense is more common, since we don't usually care too much about the physical appearance of money.

As mentioned in the comments, there are many compound nouns of the form "[something] money".

• blood money - money earned as a result of others' suffering
• funny money - fake currency (either counterfeit, or used in games like Monopoly)
• hush money - money paid to get someone to keep a secret
• easy money - money earned from little effort
• even money - 50/50 odds in a betting game
• folding money - paper currency
• mad money - money that has been set aside for personal "fun" uses
• old money - generational wealth that has been passed down through inheritance, or the families that have this wealth
• new money - Self-made people who earned their wealth rather than inheriting it
• seed money - Money invested in a startup company

In most of these [something] is an adjective, so they could be ordinary noun phrases. But the meanings don't generally involve the literal meaning of the adjectives, so these are set phrases that act as nouns.