Conclusions:
Vegetarian diets might influence risk for several cancers. The generalisability should be considered cautiously.

From nature. Interesting but not really worth the average person stressing over imo.

From the Results section of the paper:

Compared to meat eaters, poultry eaters had lower risk of prostate cancer (0.93, 0.88–0.98), pescatarians had lower risks of colorectal (0.85, 0.77–0.93), breast (0.93, 0.88–0.98) and kidney cancer (0.73, 0.58–0.93), vegetarians had lower risks of cancers of the pancreas (0.79, 0.65–0.97), breast (0.91, 0.86–0.97), prostate (0.88, 0.79–0.97), kidney (0.72, 0.57–0.92) and multiple myeloma (0.69, 0.51–0.93) but higher risk of squamous cell carcinoma of the oesophagus (1.93, 1.30–2.87), and vegans had higher risk of colorectal cancer (1.40, 1.12–1.75).

The ratios are weak and likely susceptible to residual confounding. I found it interesting that stronger numbers were from higher incidences of cancers in the vegetarian (1.93) and vegan (1.40) groups, although not strong enough considering the study is epidemiological.

The results also weren't very consistent, which likely also points to confounding. Maybe cultural or lifestyle?