There is such a thing as vegetable glycerin. That's what you want to look for. If it doesn't say, then I would keep looking. But for the most part, the stuff you get at a health food store will contain vegetable glycerin as compared to animal glycerin. It doesn't really matter too much, unless you're vegan. Most people unknowingly consume animal glycerin and gelatin all the time. Glycerin acts as a foaming agent. I would stay away from anything that says synthetic, just as a general rule, if you're trying to stay au natural.
You can use many substitutes for toothpaste, but they won't foam up. I wouldn't personally use a bar soap in my mouth because they are very harsh. You could try a combination of sea salt and baking soda, whetted down with 3% hydrogen peroxide. That would be just fine, but again, no lather. There's several different alternatives. You can use pure essential oils in your tooth powders, for their cleansing and preserving powers--but just a few drops in a batch (and NOT if you're using peroxide).
If you're serious about getting away from the stuff at the store, I recommend making all your own personal care products. A really good book with lots of recipes is "Earthly Bodies & Heavenly Hair" by Dina Falconi. It's very good, but I'm still looking for a good shampoo and conditioner recipe. Her shampoo recipes contain too much water and the ingredients separate. Since I haven't felt well lately, I've just been buying Aubrey Organics or Burt's Bees line of sh/cond., but once my energy is back, I will try her shampoo recipe again, only next time I will add an emulsifier of some sort to help it blend and thicken it up. Now if I can just find one for conditioner. I only know that the main ingredient is a fatty acid base. I just have to figure out how to make that part and then I'm set.
Well, good luck.