I've used O3 on gear for about a dozen years or so and I am convinced that it does have some benefits. I get away with things that I never could have before I started using it. Mostly a reduction in ground scent on my stand access trails. Deer just don't bust my trail anymore.
But I don't believe O3 is all that useful for laundered clothes. If clothes come out of a clean washing machine, and stored properly, they should not contain any alarming odors.
O3 is best for stuff we don't launder like boots (inside and out), vehicles, etc. I do my best to wear fresh clothes on every hunt. If I wear it, I wash it. Our laundry room has no perfume odor because we dont use that perfumed crap. After washing, I hang the clothes, turn on the O3 to minimize indoor "human" odor, and run a fan to speed up drying and help circulate the O3. If I'm away from home and have no access to a clean washing machine, then I do depend more on O3. I prefer to use contractor garbage bags, and during the treatment, I give the bag a few good shakes to distribute the O3.
I don't store anything rubber or elastic long term in an O3 environment. I have not had any obvious issues with the O3 degrading my stuff. If you need to treat clothing, IMO its best to treat just what you need for the day. Treat it, wear it, then it goes into the laundry.