Similar to most amoebozoans, the forams and the radiolarians also have pseudopods, as do some of the white blood cells of animals (monocytes). if one were to erect a taxon that included all organisms that have cells with pseudopods, what would be true of such a taxon

I believe it would be polyphyletic.
Polyphyletic groups are formed when two lineages convergently evolve similar character states. Organisms classified into the same polyphyletic group share phenetic homoplasies as opposed to homologies. The key difference between paraphyletic and polyphyletic groups is that paraphyletic contain their common ancestor, whereas polyphyletic groups do not.