H.,
I used Dreft only for my children. My first son would break out when I used Tide or Ivory Snow. (He and I are allergic to Ivory, and break out and itch if we use any Ivory products. Something in it, but I am not sure what).
I just followed suit with my second son. My boys are grown now, but I still never use Tide or Ivory products.
If you can, seperate the baby's clothes out and use a product that does not have dyes, perfumes, or any other harsh chemicals until about the age of two. At about that time their immune system is up to snuff and the baby is less likely to develop allergies from the chemicals in detergents (or anything else).
Good Luck with your new baby!