I think another one of the probs with bleach is that one of the byproducts of cholorine bleaching is dioxin, which is a known cancer-causing agent. If I use disposable feminine hygiene stuff I use peroxide-whitened.
For the dishwasher I alternate the 7th Generation stuff and conventional, as the 7G stuff doesn't do as good of a job, unfortunately, so i alternate them. I use non-chlorine bleach from 7G for my whites and it works just fine. I've used Country Save non-chl. bleach, too, with good results. I used the Tilex mildew stuff when we moved in
but the "root killer" stuff works really well, so I haven't had to redo it. I keep it up with the Method shower spray.