As I understand synthetics, 100% synthetic oils are no longer petroleum as they have been synthesized, changed molecularity, however, they may or may not mix with and thus soften black powder fouling. That is the stickler - the lube must be compatible with black powder fouling. Vaseline is not a petroleum oil, it is a
petroleum wax & when mixed with beeswax, roughly 60:40, it makes a terrifically great bullet lube for muzzleloaders or ctg. guns. In my rifles of both ilks, the equal of SPG and that says a lot.
edited - changed the word "lube" to "fouling" -in the first sentence. I guess I was typing faster than my mind was running, last night.
Partial synthetics are a blend of synthetics and petroleum - maybe. Years ago, there was some marketing speculation that some people might accept synthetics if a partial blend, rather than being labeled 100% synthetic, even though those so marked were (likely) 100% synthetic.
Petroleum oils do not mix with/soften BP fouling, which is why petroleum oils are not recommended for lubes, for BP shooting. The whole idea of synthetics was their molecules had a greater compressive strength than-did petroleum oils, and also higher burning and flash points levels - thus they lasted better in high heat conditions, along with not "wearing out" as quickly as petroleum oils, thus "lasting" longer. That is how I understand the synthetic/petroleum wars.
So - a synthetic might work, or not, depending on how it reacts with BP fouling, as in, will it soften and mix with the fouling, or will it remain a separate solution and not mix - THAT is the question.
I suspect some will, some won't.