1) I'll rinse it - inside and out, usually in the shower, and most often after getting out of a swimming pool.
2) I'll wash it - add a capful or two of the antiseptic concentrate Dettol, which unlike LOC doesn't leave suds to be rinsed out.
I first heard the use of Dettol recommended by spearfishermen for cleaning their wetsuits - it seems that fish can't smell the stuff!
PS For my boots I often use a capful in each. It's so effective that my old boots can actually come out with a faint odor of their original "fresh neoprene" scent!