Just wondering, what happened to the perfectly good and useful word - “organelle”? Ah, I have answered my own question. Some restrict “organelle” to a cell structure with its own lipid membrane, ruling out the flagellum.
There has been a burgeoning subfield of studying membraneless organelles. Usually they rely on some sort of phase separation. This works much like oil droplets in water, but there are several mechanisms for doing this that do not involve lipids (or oil) at all.
A large number of membraneless organelles, including nucleoli, Cajal bodies, P-bodies, and stress granules, exist as liquid droplets within the cell and arise from the condensation of cellular material in a process termed liquid-liquid phase separation (LLPS).
By this criteria, I’m not sure flagellum are organelles, because there is no phase separation. However, we can certainly find references to the flagellum as an organelle. Maybe it is. It is a matter of definitions:
It’s not hard to find references referring to ribosomes as organelles. (Though it’s also not hard to find references saying they aren’t organelles.) And so we have another term with multiple definitions.