“Democrat” is the singular noun form, “Democrats” is the plural noun form, “Democratic” is the adjective form, and “Democrat”-as-adjective is the “signal that the speaker is a hostile partisan" form. They are all useful distinctions.

> While some people get upset about it, "Democrat" is useful to differentiate the two verbally. Obviously capitalization isn't possible.

Not really. "Democrat Party" is literally just a shibboleth used by opposing partisans who are upset that "democratic" is an adjective with positive associations. Everything else is just a post-hoc rationalization.

You think that because a) you don't know the origin of the intentionally incorrect usage of "Democrat" as an adjective, and b) you're confused about the difference between an adjective and a noun.

The usage in that domain name is as a noun. "Joe is a Democrat" is fine. That's a noun. "Democrat politicians" is not fine. That's an adjective.

I would note the pattern is not unique to "Democrat/Democratic"; it is used to turn other descriptors into slurs. Cf. "Jewish" vs. "Jew" as adjectives.