About the rubber, in itself, it could be relatively inert for life, but the main concern comes from the added chemicals. Not those involved in the vulcanization, as they are pretty locked in the rubber matrix, but the protectors against oxidation and eventually some various softeners. The last ones don't stay in place as they don't belong to the rubber matrix but are here to weaken it, like the soft PVC.
An unprotected rubber would crack and decompose in a few years, by the oxygen wrecking the rubber' molecules. See what you got with the cheap tyres for wheelbarrows and lawnmowers. To avoid that, they add certain antioxidants with two properties : catching the oxygen before the rubber does (but that depletes its own concentration at the surface), and having a great capacity of diffusion in the rubber to replenish the surface's concentration from the internal rubber mass.
So you got a constant supply of this shit at the surface to do the protecting job. That's good for the rubber's life but not for the biological life.
I don't know if you heard this story before but here it is ( it comes from my Dad who is an organic chemist): The (pro)truckers were often in big trouble with their hands, showing some dermatitis, allergic reaction or skin cancer (I don't recall precisely). It get so important that that was acknowledged as a professional disease. Ok, but they can't tell why the truckers where affected. Until they looked closely to the habits and customs of the said truckers. And they found it.
The truckers are very worried about their tyres (usually), it's understandable. So, after a travel, they used to keep a check on the tyre's temperature by putting an hand on them, a quick and easy test... and each time, they got on their skin a small amount of these chemicals. Moreover, the tyres were hot by the travel, so the chemicals penetrated easily in the skin. Day after day, weeks, months, years, the constant irritation messed their hands.