PLEASE READ THIS! This is a table of them: https://i.postimg.cc/tgFVZcW8/table-of-elementary-particles....

When you say “inherent property” I think “immutable” as in “cannot be changed from one chirality/spin to another”.

Is that a useful line to draw?

Not a physicist. Never played one on TV.

Chirality is a real property of (most) elementary particles. For example the electron with left chirality has a weak hypercharge of -1, but the electron with right chirality has a weak hypercharge of 0. https://en.wikipedia.org/wiki/Weak_hypercharge#Definition In some sense, they are very different particles. Also, only the left version interact with the weak interaction.

chirality is how particles get mass - the Higgs field gives fermions mass by coupling their left and right-chiral parts, causing chirality mixing