Realists, like cladists and particle physicists, think (thus actually assume as an axiom) that classes can be handled logically as “things”. Cladists, for example, think that it doesn’t matter what their “species” are, they can be anything for the cladistic reasoning about “trees” for such “species” to be logically consistent. However, exactly this is the problem, because nothing can be everything! Especially, “classes” can’t be “things”, because the class “class” is orthogonal to the class “things” per definition. It means that realists are fundamentally contradictory (ie, per definition). They thus either don’t understand what they do or are consciously contradictory, hard to tell which.
The consistent way to handle classes is instead by first-order logic, as Russell’s paradox and axiomatic set theory (like ZFC) shows. This is also what the Linnean system for classification of the biological diversity does.