Jews can wear clothes made from non-kosher animals, so burning them in a car engine should be fine. Granted, not all rabbis agree with this and there is considerable controversy about Jews raising pigs, for example. But in general, the prohibition is against eating non-kosher animals and nothing else. The prohibition against touching pig carcasses is generally interpreted to mean only during specific holidays.
With Jews the pig problem is largely that of eating them. While you can always find an outlier if you look for one, using non-food products derived from pigs is not usually prohibited. Although having one as a pet would be quite unusual.
Muslims are more pig-averse than Jews, their religious laws prohibiting not only eating but using things made from pigs, touching pigs, being near pigs, and pig imagery.
I don’t see Jews having a problem with pork-derived biodiesel but I suspect Muslims would be reluctant or entirely opposed to it. Well, the observant ones - there are secularized Muslims, too.
I’m no expert in either Kosher or Halal, but I believe unintentional contaminates in food doesn’t disqualify it. i.e. water in NYC is technically not Kosher (or vegan) due to small crustaceans in it, however it is considered Kosher by intent regardless of it containing unclean animals.
When those “crustaceans” (specifically copepods) were not known to be there there was no problem but once discovered then it very, very much was a big deal to the more Orthodox communities in New York City. It was a very big deal to a lot of people who wound up installing water filters or moved to exclusively bottled water. If the water contains unclean animals it is unclean water for purposes of consumption. Nothing “technical” about it for those folks.
I recall some Rabbis believing that children should not have certain pets. I always thought they believed the family may inadvertently consume some portion, like hair.
It had occurred to me that vegans, who eschew ALL animal-derived products like leather and certain cosmetics, would have nothing to do with lard-based biodiesel.
Jews and muslims might reject biodiesel on the same criteria.
Lest a conscientious bio brewer marketed a “plant only” brew of bio…and market it at a premium, the way Organic Food is higher priced.
Considering all those Torah scrolls, apparantly the question occurred to some people whether you may write them with ink that involved (non-Kosher) wine or oak galls: https://stamforum.blogspot.com/2012/02/ink-kosher-vs-non-kosher.html
They seem to be arguing about it, but basically yes?
Kashrus rules (with a few small exceptions) deal only with eating and drinking. There is no problem with a Jew using biodiesel in his or her car or other internal combustion engine.
As someone who is currently writing a Sefer Torah, I can address this.
There is a general rule that anything used in the making of tefillin, mezzuzos and Sifrei Torah have to be “min hamutar b’ficha” (made from that which is permitted to your mouth – i.e. kosher animals).
However, that restriction only applies to the species and not the individual animal. So, for example, if you have a cow that died without slaughter, you can use it’s skin for these purposes, even though the individual animal is not kosher to eat.
This law is something that is particular to the writing of Sifrei Torah, tefillin and mezuzos, and does not really apply to kashrus law.