I have been using an HE washer for several years, and I have used HE detergent and regular - probably in every commercially available brand to see what works well with our water to clean our clothes at the least expensive cost.
You CAN use regular detergents and additives, but you need to reduce the amount (as other folks have stated). I usually adjust by half. Our water is rather hard, so I gave up on powders because they do not seem to dissolve completely - with the exception of oxi-type cleaners (you can use generic brands and they work just fine) and Biz. I usually add these directly into the load (sprinkling it around) before I start the cycle.
It is also true that Dreft and Ivory detergents are not really necessary for babies unless your family has a history of skin sensitivities. Most products are safe and gentile enough for infants and my pediatrician has backed this up.
My family does have skin sensitivities, so I used Dreft for my first child. When I learned more about detergents, I tried my regular detergent on my second child's clothes and we had no problem. I did a test for the 3rd, too (just to be safe), and again no problem. It sure was nice not to have to separate and run a small load in my big HE for the infant clothes anymore.
I come from a family of 8 kids with 7 of us owning HE washers now, and we all use the oxy-type additives and regular detergent
(unless HE is on sale)- with no problem.
So, my recommendation - stick with what you want to use, just reduce your amount by 1/2 for non-he detergent of what you would regularly use, otherwise, watch for sales.