“Slurring” guests are usually not drunk

“To slur”, applied to speech, either refers to running syllables together, or disparaging a person.

In the first (intransitive) sense, “he slurred during that conversation” would be correct, meaning he ran his syllables together.

In the second (transitive and less common) case, “he slurred John” would be correct and would mean he disparaged John.

When the word “slur” refers to a word or phrase that is widely considered offensive to a group, it is a noun. “He used a slur”, or “he made a slur”.

Claiming that every racist guest who drops a slur is “slurring” amounts to critiquing their pronunciation and not the content of their speech.