Can poor hygiene cause prostatitis, epididymitis, or other infections?

Not likely. Not likely related to prostatitis or epididymitis. Can't really comment on 'other infections', other than to say that skin infections like infected hair follicles, sweat glands or infected sebaceous cysts can be associated. Fungal infections can thrive even if hygiene is great (socks before undies may help). Goes to be said, that good hygiene is rarely a bad thing.