I was in university when carcinogens were said to be contained in pork and red meat. The idea is that carcinogens cause cancer.
The main thing I have to say about this is: the idea is far and away overblown, and there are two main reasons for this.
The first reason the idea got overblown, for what it actually is, is because the fields of study for this sort of thing rarely have any groundbreaking research, so when they get something they really try to hype it up. I believe the relevant fields here were biology and the medical field. Having been on a campus where intellectual property theft is rampant and everyone thinks they're going to be a famous scientist and "win all the marbles" for something this is definitely something they'd do, and they were trying to cause as much fear in the student population as possible.
The second reason is because of synergy from people who have radical views on what foods should be consumed, like vegans. Vegans are almost always far left liberals, and as can plainly be seen in Europe and other European countries, like America, Canada, New Zealand, Australia and South Africa, anyone part of a far left constituency has clout in the media, and so these sort of things get overblown.
What about the assertions from the research overblown, you may ask? The amount of carcinogens in these meats is so low that one would have to eat several pounds of meat **in a single sitting** to begin to have a minuscule chance of getting cancer. There are people all over the world who eat a lot of meat as a large part of their diet, especially in European countries like America, and not until this research showed up did anyone even suspect they could get cancer from it? That common knowledge should be enough to convince anyone that this research is negligible.
I, for one, have year streaks where I eat 1 to 2+ lbs of beef steak nearly every single day of the year (my freezer is packed with beef). I have regularly gone to all you can eat buffets and eaten about 2.5 lbs of beef steak each meal. My dad has done the same thing, and the only difference between he and I is that I've maintained a normal weight and a muscular build, while he is fine with being obese (hey, at least he doesn't make excuses for why he's obese). Anyways, most of my family is like this, and no one has had cancer in my family, ever. And certainly not bowel cancer, and, again, one would have to eat a significant amount of meat to have so much as a minuscule chance of increasing the likelihood of getting cancer.
No one should do anything whatsoever to "avoid" the carcinogens in pork and red meat. Your chances of getting cancer are so low that I don't think there is a single confirmed case. However, nowadays, the science fields are more of Science™ fields than anything else, and information coming from authoritative sources should be heavily questioned, especially when political influence occurs related to it. Or if there's a financial incentive for someone who's already rich and powerful; this almost always guarantees that any radical notion is worth ignoring, as there'd probably be a gradual build up instead.