Note: Post edited on 27th august 2018 to reflect my recent research.
The quest of the perfect toothbrush
Choosing a toothbrush… For most people the choice can be resumed in selecting the hardness and maybe the quality of it, plus some marketing clever tricks.
If you are vegan or vegetarian, you will also want it to be cruelty-free. It sometimes contains pork silk if you buy organic, for the bristle. If you are also ecologist and want to avoid petroleum-based products, your choice just reached zero. It's either nylon or pork silk. Some sellers advertise that you can put the nylon bristle in the compost, but I’m not a big fan of letting plastic degrade in nature. Plus, some of them are lying on the type of nylon and not all of them will degrade anyway. Others are blurry about the material of the bristle, mentioning bamboo, but only the charcoal coating is bamboo, not the bristle itself. Sellers are surfing on the ecologist wave, sometimes for the worse.
Switching to siwak
Another solution is to quit the classical toothbrush and go for siwak, which is just a piece of wood. In theory, any kind of non-toxic wood with the proper texture will work, but the one usually used for that is siwak. You cut a little bit of the bark on a thin branch (around 5mm), chew it a little bit and brush your teeth with it. No toothpaste required. When it becomes too soft or after two or three days, just cut it and start again. You will probably need a few days to get use to it, as any habits and beliefs getting turned upside down.
Now, I actually feel my teeth are smoother after using a siwak. I had to come back to toothbrush several times. At first I was still preferring the toothbrush but then it started to feel more aggressive and unnatural. I noticed the mint smell was leaving very quick and giving a false temporary sense of freshness. I could not clean the rest of the mouth as well with a toothbrush. It's less bulky when travelling, I don't need toothpaste, I can replace it for free with any edible wood if needed. It's 100% natural and you can even get it locally.
The perfect vegan and petroleum-free toothbrush?
To summarize, the perfect vegan and petroleum-free toothbrush doesn’t exist yet. The only solution I found was siwak, or wood, but it can be challenging for travellers and not necessary environment-friendly to import siwak to your country. And again, check the wood you are using is not poisonous!