My family has a long history of cancer, but that's from the smoking, not from the meat. Our digestive tract never even gets any cancer even if cancer occurs and spreads to everything else. We eat meat on the order of several pounds per day, and never had any issues.
I personally have a minor allergy to some pork products, however I think it's either the preparation method or something to do with the antibiotic injections/preservatives they use since it's not all preparation methods, or pork sources. (like a local private farm's pork seems to not trigger it, but almost all bacon or ham does)