There is very little research done as filing in a prospective research study on something that is potentially harmful for human baby is virtually impossible due to all the ethical issues. The little research there is comes from follow-up studies and statistics that docs gather here and there.
Also, every brand of hair dye is different and uses different chemicals, pigments and fixatives so it is really hard to generalize.
Moreover, lowering the bar on hair dye safety, tanning, etc and other cosmetic products or procedures during pregnancy is in the interest of the industry, as they can simply sell you more. So always consider that aspect too when the take on certain things changes.
It could be that in the earlier years, hair dyes used more toxic components and were potentially harmful to the baby and that now they are forced to eliminate some of those, so new generation hair dyes are safer. what i'd do is google up for MSDS (Material Safety Data Sheets) of the hairdye components and then judge for myself.
ie. this is the PPD one, the most common hair dye component of synthetic hair dyes (natural herbal ones usually don't contain it but standard ones do): https://www.sciencelab.com/msds.php?msdsId=9926499
the sheet refers to the pure product, of course, not when mixed with other stuff and the ultimate toxicity as for any other thing depends on the dosage and amount of exposure. this to say, hair dye won't kill you like it didn't kill anybody so far. but to say it is totally safe and harmless... that's another pair of shoes.
