Well, certainly regular chlorinated water kills some stuff. That's why we have chlorine in our water in the first place... Not sure how sensitive plants are to it, but I think not very?
Other things, like ich, only survive if they have fish to attach onto. So if you keep them in quarantine (at aquarium temperatures so it goes through its life cycle) and rinse once in a while for a few weeks, they'll die off.
I've never tried using potassium permanganate (which is supposed to be less harsh on plants than bleach but tricky to work with). I did do a bleach dip on my next set of plants (anubias, water sprite, water wisteria, and pennywort), but it was super quick and dilute, and none of those plants are supposed to be bleach sensitive. Mostly I just quarantined them... and a couple of snails still got through.
To be fair, a lot of people have used store plants with just a quick rinse and been fine! ANHEL and I are just paranoid... Maybe someone else will chime in with an easy way to disinfect =)