Well, if you want to get technical, petroleum IS organic...

Seriously, though, even if those shingles did leach, the effect would be extremely localized. You might get some contamination of the soil directly below them if there's no underbed, but unless they're IN your plot, I don't see any way that you could suffer any health effects.

Gravel isn't a workable alternative (think about how hard it is to ride a bicycle in loose or newly-laid gravel) and woodchips are probably worse. You need something that's smooth, firm, doesn't move, and can handle getting wet repeatedly. About the only good alternative I can think of would be a well-built wooden or masonry pathway. However, you might get more practical suggestions in the Accessible Gardening forum, if you haven't already asked there.

So I would say that the social benefits of making the garden accessible outweigh the "un-organic" nature of the shingles. If they really bother you, volunteer to replace them with a wooden pathway, but that would cost you lots of money. Definitely avoid complaining about the shingles if you haven't offered an excellent alternative (preferably one for which you're willing to do all the work personally), or you'll come off looking like you're against equal opportunities for people with disabilities. It's a matter of weighing the benefits against a very tiny potential risk.

We use upside down old carpeting strips in our garden, and I can imagine that they might provide traction as well as being a weed barrier, especially if they were held down with strong landscaping pins.

what about recyled tires or slate chips?
any idea how i might get my hands on those.
other people in my community are suggesting them as an alternative.
thanks.

Here are two ideas:
1. Use salvaged bricks from structures about to be torn down; you will have NO trouble finding a wealth of these possible sources. Contact a local sand blasting company and ask for free sand to fill in between the bricks, once they are laid out in a contained pathway. Be sure to level the pathway before you lay the bricks.

2. Salvage wood from the same type of structures. 2x4's (or 'beefier') are good for a solid, load bearing surface. Again, level the pathway, put some sand underneath, have a frame (of 2x4's or 2x6's) and expect to replace boards every 2-5 years.

Good Luck!