OP I really, really don't think 'they' have proved that eating meat and dairy causes cancer.
I'm not an oncologist but my best friend is one.
When we discuss these things (usually over a slow-cooked meat and a bottle of red) she tells me that most cancers are 'caused' by genetics/sheer bad luck.
Yes, your risk of getting bowel cancer, colon cancer etc goes up if you eat a lot of meat and smoked foods.
For sure, your risk of lung cancer shoots up if you smoke.
This does honestly not mean that all cancer (even most cancer) is 'caused' by eating meat. Or dairy. In normal, moderate amounts. Alongside salads, leafy greens, fruit, cereals, carbs, fibre. Etc. A balanced diet.
I'm sure someone who actually knows the detail will be along to explain this further, but it's quite wrong to think/declare that meat and dairy 'cause cancer'. No, they don't. Even in HUGE amounts, I don't think anyone with a science background would say they 'cause' cancer. And most people don't eat HUGE amounts of any one food group, do they?