Great questions and I'm really happy you are trying to get more information when you see conflicting results. This is going to be a long answer for a complicated issue.
You should always use the chemical ID associated with the product you are using, because manufacturers develop SDSs based on their product. This is especially true with things like petroleum distillates which can be any variety of mixtures and naphtha might be one of the best examples of a totally ambiguous term.
Having said that, manufacturers are not required to do their own testing and rely on available data to come up with their hazard warnings. In fact, Gamblin's SDS even says, "Specific toxicity tests have not been conducted on this mixture. In accordance with OSHA’s Hazard Communication Standard 1910.1200, this mixture is assumed to have the same health hazards as its significant components." Each manufacturer uses their own algorithm/system to come up with their warnings, so that may be why you see discrepancies between manufacturers depending on which H&S information they include.
The unfortunate reality is that health and safety data on MOST chemicals is pretty limited. Section 11 of the SDS will give more specific toxicological information if there is any. But you might see phrases like: "No components of this product above the declaration level of 0.1% have been identified by IARC, OSHA or NTP as carcinogenic." This doesn't mean it's not carcinogenic.There just isn't any data to say that it is. Information from the IARC (International Agency for Research on Cancer), the ACGIH (American Conference of Governmental Industrial Hygienists) and OSHA can give you a much better picture of the current understanding of chemical than the SDS might.
There are also big differences between European and US standards with European standards tending to be more cautious (if that's the right word). The example you give of a 1B hazard means there is evidence to suggest that the material causes cancer in animals, but not humans. This doesn't mean it does not cause cancer in humans, there just aren't any studies to prove it.There are also no links to the studies that have resulted in that classification. Sources like Toxnet and Pubchem, which provide links to peer-reviewed sources, can be extremely helpful. Were animals fed the material? Was it rubbed on their skin?
Why does that matter? Because it's important to understand HOW something is a carcinogen. Chemical health hazards are highly dependent on type, dose and route of exposure. Routes of exposure can be inhalation (breathing), absorption (through skin, eyes, etc) and ingestion (eating). How are you exposed to this chemical? If something is carcinogenic from eating it, then your art materials are lower risk because if you're washing your hands and not eating while working, then you're less likely to be ingesting it. However, if it is carcinogenic from breathing it, then you are more at risk standing over a painting, brushing it on and breathing the vapors.
Asbestos is a good example. It's a well-known carcinogen--if you breathe it in. Mercury is another example. Organic mercury, the kind found in fish, is primarily a health concern when you ingest/eat it, while elemental mercury, the kind found in thermometers, is primarily a health concern if you breathe the vapor.
The bottom line is to always err on the side of caution. If there is lack of definitive evidence that something is safe, than always use the highest level of personal protection possible (ventilation, gloves, goggles, etc.). I personally would not be using this stuff with without proper ventilation or a respirator. It's pretty clear that petroleum distillates are central nervous system depressants and can make you nauseous and dizzy and that's enough for me to take precautions, even if it doesn't cause cancer. People safely use these chemicals all the time--they are low risk with proper precautions.
Some good resources on artist material hazards are:
Arts, Crafts and Theater Safety: http://www. artscraftstheatersafety.org/
The Artist's Complete Health & Safety Guide (Book)
Artist Beware, Updated and Revised: The Hazards in Working with All Art and Craft Materials and the Precautions Every Artist and Craftsperson Should Take (Book)
Kerith Koss Schrager