What exactly is a white supremacist?

At one time it referred to someone who believed that “white” was a distinct sub-species (rather than a pigmentation) consisting of European whites but excluding non-European whites (e.g. Jews, Arabs, East Asians etc.) and who also believe that the “white race” was superior to any other. A variant of this was the Nazi movement which tried to link the Indo-European (Aryan) language family to a purported “white race”. Note that many ethnic groups have “white” skin but were excluded for cultural or political reasons.

Among Democrats, it means anyone who disagrees with them.

You needn’t take the comment literally. Clearly what he means, and correctly at that, is that Democrats falsely attack their political opponents with the charge of racism at every nebulous, or less, opportunity.