There is no evidence that synthetic chemicals are more harmful than those produced by nature
One of the problems with the debate about whether artificial chemicals (which could mean novel compounds or naturally occurring compounds synthesised by laboratory or industrial processes) are carcinogens is that the tests on artificial chemicals are rarely seen in context. Bruce Ames summarises the issue well in the abstract of one of his papers (my emphasis):
Toxicology studies of synthetic chemicals at high doses must be viewed in the context of the world of natural chemicals, which make up the vast bulk of the chemicals to which humans are exposed. In tests at near toxic doses (e.g., the maximum tolerated dose), one-half of all chemicals, whether synthetic or natural, are carcinogens; one-third are teratogens, and about half are clastogens. Natural and synthetic chemicals are similar in their toxicology, and at the low doses of most human exposures where cell-killing does not occur, the hazards may be much lower than are commonly assumed and often will be zero.
Bruce Ames can claim some expertise in this area as he is the inventor of the well-known Ames Test, a cheap way of screening chemicals for their mutagenicity.
His work is smmarised well in a NY Times blog in 2007:
But Dr. Ames began rethinking this war against synthetic chemicals after thousands of chemicals had been subjected to his test. He noticed that plenty of natural chemicals flunked the Ames test. He and Dr. Gold took a systematic look at the chemicals that had been tested on rodents. They found that about half of natural chemicals tested positive for carcinogencity, the same proportion as the synthetic chemicals. Fruits, vegetables, herbs and spices contained their own pesticides that caused cancer in rodents. The toxins were found in apples, bananas, beets, Brussel sprouts, collard greens, grapes, melons, oranges, parsley, peaches — the list went on and on.
...Even though these natural chemicals are as likely to be carcinogenic as synthetic ones, it doesn’t follow that they’re killing us. Just because natural pesticides make up 99.99 percent of the pesticides in our diet, it doesn’t follow that they’re causing human cancer — or that the .01 percent of of synthetic pesticides are causing cancer either. Dr. Ames and Dr. Gold believe most of these carcinogenic pesticides, natural or synthetic, don’t present problems because the human exposures are low and because the high doses given to rodents may not be relevant to humans.
“Everything you eat in the supermarket is absolutely chock full of carcinogens,” Dr. Ames told me. “But most cancers are not due to parts per billion of pesticides. They’re due to causes like smoking, bad diets and, obesity.”
Ames and Gold summarised the evidence about pesticide residues in food (a highly controversisal area but one where the results have much broader implications for artificial chemicals in other contexts) in a chapter of the Handbook of Pesticide Toxicology (pdf available online here):
Outside the workplace, the levels of exposure to synthetic pollutants or pesticide residues are low and rarely seem toxicologically plausible as a causal factor when com- pared to the wide variety of naturally occurring chemicals to which all people are exposed. Whereas public perceptions tend to identify chemicals as being only synthetic and only synthetic chemicals as being toxic, every natural chemical is also toxic at some dose, and the vast proportion of chemicals to which humans are exposed are naturally occurring.
There is, however, a paradox in the public concern about possible cancer hazards from pesticide residues in food and the lack of public understanding of the substantial evidence indi- cating that high consumption of the foods that contain pesticide residues—fruits and vegetables—has a protective effect against many types of cancer.
Later in that chapter they argue:
Current regulatory policy to reduce human cancer risks is based on the idea that chemicals that induce tumors in rodent cancer bioassays are potential human carcinogens. The chemicals selected for testing in rodents, however, are primarily synthetic. The enormous background of human exposures to natural chemicals has not been systematically examined. This has led to an imbalance in both data and perception about possible carcinogenic hazards to humans from chemical exposures. The regulatory process does not take into account (1) that natural chemicals make up the vast bulk of chemicals to which humans are exposed; (2) that the toxicology of synthetic and natural toxins is not fundamentally different; (3) that about half of the chemicals tested, whether natural or synthetic, are carcinogens when tested using current experimental protocols; (4) that testing for carcinogenicity at near-toxic doses in rodents does not provide enough informa- tion to predict the excess number of human cancers that might occur at low-dose exposures; and (5) that testing at the maximum tolerated dose (MTD) frequently can cause chronic cell killing and consequent cell replacement (a risk factor for cancer that can be limited to high doses) and that ignoring this effect in risk assessment can greatly exaggerate risks.
The book is a rich source of links to the primary evidence.
In summary: when naturally occuring chemicals are tested with the same protocols as "artificial" chemicals roughly the same proportion emerge as possible carcinogens. This suggests that "natural" is no better than "artificial". The results are not likely to be significant for explaining most cancers in people.