|I'm no big expert on this but I think that the biggest safety concerns when dying are either inhaling the dye powders and/or soda ash. Obviously you don't want to ingest either one either... From what I've read on the Dharma website, those are the biggest risks.
Obviously I think it's pretty safe or I wouldn't do it. You do rinse the fabric quite a lot to get rid of excess dye so anything 'left behind' is pretty minimal and the vast majority is permanently bonded with the fabric fibers. I think some people are concerned with the environmental (and therefore long-term for our health as well) effects that the dye and dye chemicals have. As long as the fabric is well rinsed though, I don't think there's really much risk that dyed fabrics will irritate skin. We all wear dyed clothing (including intimate stuff like bras and underwear) all the time, I think that's about the same thing...
I think if you have any particular concerns, I'd email Dharma about them and see what they say. They have amazing customer service! And although it's true that they will probably have some bias since they do sell the stuff, they tend to be honest enough that I'd have a good amount of faith in what they say.
Obviously the absolute safest and most environmentally sound way to dye fabric is to use natural dyes (derived from plants usually). If you can eat the stuff, it's a pretty sure bet that it's safe! Of course, the only 'problem' with natural dyes is that the results are unpredictable (could be streaky, blotchy, too light, and can often fade rather easily). It can be a fun experiment though, especially if you have older kids that would think the process fun.