I wish I knew for the toothpaste... I haven't been able to find anything safe for DD yet. So for now, we just don't use anything (she's 29mo). Eventually I suppose I will have to start researching though... For myself, I use EcoDent.
For soap (for DD)- we use California Baby, but we only use it about once a week (or if she gets into something really dirty)- otherwise we stick with water. She is IgE to corn and coconut, both of which are used in CA Baby, and it doesn't seem to bother her. But they don't use any top allergens in their products, like nut oils or dairy.
Corn is so hard. I avoid all processed foods so that we don't get any trace corn, but I've long ago given up on avoiding all environmental exposure- it's just not possible. Everything is made of corn- carpet, toilet paper, paper cups, you name it. And most (all?) "natural" home products- detergent, cleaning stuff- is made from corn/coconut. So I guess you have to judge how severe the allergy is- just watch for contact reactions if you use any products containing corn.
Mom to DD1 (10/07) and DD2 (3/11) I blog about our life with food allergies and eosinophilic disorders.