Your linked source claims processed meats can cause a 18% increased incidence of colorectal cancer. The CDC [0] says rates of those cancers are 36.5 per 100,000, or 0.03%. Since some of those people undoubtedly eat processed meat, lets assume the cancer rate is 0.025% for people who don't eat processed meats.

For me, those numbers really dont move the needle - its highly unlikely to get colorectal cancer and abstaining from processed meats doesnt really change the rate much at all. There are probably other good arguments in favor of not eating these foods, but cancer doesnt appear to be one of them.

[0] https://www.cdc.gov/cancer/colorectal/statistics/index.htm