I am so happy my package arrived! I found this website when doing a search for undyed organic wool and they have no idea I am mentioning them here, so did not sponsor this in any way. Check back soon for more details, but for now, check out the pictures.
Here are links to some completely safe yarns:
Here are some links I found in my research about dyes:
(So far, my conclusion is that fiber reactive dyes, a specific kind of synthetic dye, are actually safer than natural dyes.)