|I'm not sure what fabric softener would do. You're not supposed to use it with diapers because it can cause them to repel, but that's not really a concern with covers. Although it probably wouldn't affect function in terms of keeping things in, I guess my concern with softener is that it would clog the pores and affect the fabric's breathability, which could keep things a little warmer, maybe not be as good for rashes.
I'm not sure about the non-chlorine bleaches. Occasional use may be fine, but it's probably not something I'd use regularly--but then mostly I just don't add things! :-)
Why are you looking to use these products? Just wanting to throw the covers in with another load that has non-chlorine bleach and softener? Or?