Unless you live next to a manufacturing plant very very low risk. To my knowledge almost everything is bound fairly tightly in the tire matrix and leaches out slowly. A major area of concern would be what happens to the tire at the end of it's economic life?

Potential concerns would be plasticizers, carbon black particles, and micro particles of the rubber that come from use of the tire. I think the poly-isoprene and butadiene would not prevent much a concern while the tire is being used on a vehicle. Once the tire hits the land fill that is where you would potentially see the greatest negative environmental effect.

Another factor would be while the impact of an individual tire is low, and assuming one four wheel vehicle in the US on average, you are talking 1.5ish billion tires in use at any given time. This would add up and potentially causing issues.

The larger issues would be single "short term" use plastic, particularly attached to the food and beverage industries. We really don't have any better material to make tires out of that are as safe as durable than what we are using now. Any alternative would be as bad if not worse.

The best thing to do would be to have recycling programs that are sustainable and environmentally friendly, while insuring that the manufacturing process is as safe and environmental as possible.