My uncle has spent a lifetime researching this sort of thing, he is a colour chemist and has worked on ink, clothing and hair dyes. (he once made the queens eyes glow red in a mock up bank note when he was working on security features, he's done some very cool stuff.)
One thing he said to me a while ago was that there was a chemical used in hair dye that was banned in the textile industry decades ago, because of these links.
He has researched the link between hair dye and cancer and it is definitely there, I think he said something about certain chemicals absorb the pollutants in the atmosphere that then cause the link, but my O level Chemistry was a very long time ago.
I do know his research came across some resistance from the big corporations, who he has also worked with from time to time.
The more research that goes on the more we find out, does anyone remember the green styling gel we all used in the '80s. My parents (notorious hoarders) still had my old jar, almost empty, in the bathroom we looked at the ingredients and it had formaldehyde in it!!!
There's no denying that millions of people use hair dye daily (including his own DD) and are absolutely fine, but that doesn't mean for some the link isn't there.