All the time. I've taken it off to run it underwater, but most of the time I just pull my homemade harness up to my midsection and wash it like that. It gets clean in the shower with me, I don't even take it off to dust it. I just do like people do with baby powder.
After determining it was safe (and finding my condom-of-hairgel an unworthy alternative), I even began swimming with my packer.
It makes me considerably less dysphoric.
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Andrew, have you tried making your own harness? I use a thin-ish ace bandage and a hair-band.