Learn Turkish: Hiçbir azınlığı dışlamak doğru değil. - It is not right to exclude any minority.

It is conceptually very similar! Both involve turning a noun or adjective into a verb to express an attitude or behavior toward something. However, dışlamak uses the extremely common -lAmAk suffix rather than -(I)msEmEk. It is built from dış (outside), so dışlamak literally means "to treat as outside," which we translate as "to exclude" or "to ostracize."

How is azınlığı built, and why does it have an accusative ending?

The root is az (few/little), which becomes the noun azınlık (minority). Even though hiçbir means "any" or "no" in this context, the entire phrase hiçbir azınlığı is still the specific direct object of the verb dışlamak. Therefore, it takes the accusative suffix -ı, and consonant mutation softens the final k into a ğ.

Could we say hiçbir azınlıkları if we wanted to translate it as "any minorities"?

No. A strict rule in Turkish is that the word hiçbir (no/any) must always be followed by a singular noun. Even if the English translation sounds perfectly natural in the plural ("It's not right to exclude any minorities"), the Turkish noun must remain singular.

How does the grammar of "is not right to exclude" work here?