Thank you for your question and I understand your concern.
No, you do not have to go out and purchase new bleach and fabric softener specifically designed for HE washers. You do not have to use He bleach or HE fabric softeners. If you use standard fabric softeners be sure to dilute it first before putting it in the dispenser if it's the thicker type. Also buy in small containers and not the large because overtime it can thicken and settle to the bottom before using it all.