Note that some of these are studies and some are lit reviews (skimming other studies), and none does more than identify a correlation.
It could turn out that one or more of these foods has a direct causal effect on prostate cancer, but that would be a long way off. It could also turn out (and probably will, in most cases) that the kind of men who eat a lot of meat, eggs, etc are the kind of men who are more likely to get advanced prostate cancer because of some shared unknown factor, which wouldn't go away if they stopped eating them. In Dr Walsh's book, the one food that seemed to be accumulating enough evidence for a definite go-light recommendation was processed meats (bologna, hot dogs, etc). Again, not never, but go really easy them.
FWIW, I've been vegetarian since 1997, and was still diagnosed with de-novo stage 4 prostate cancer in 2021. Using moderation with high-cholesterol foods like meat, eggs, and full-fat dairy is a good health choice regardless, and we do know that obesity appears to have a strong correlation with many cancers, but I don't think we can control our own cancer destinies by cherry-picking isolated studies and lit reviews and chasing them. Our best bet is to eat a healthy balanced diet, stay active, and stick to our treatment (getting second and third opinions when necessary).
Well yeah, I have been at many meeting where correlations are used and some correlations are really strong when data is mapped out and statisticians come in. What do you want somebody to hit you on the head, just kidding of course but I don't think what we are looking at is cherry picking either. Obviously we should do whatever we want, and that is the way medicine should go, patient decides path, but sometimes correlations help (and not just fire engines at fires). I chose Tulsa Pro 1.5 years ago, but no docs are advising Tulsa just yet till something hits them in the head and gives them the machines and training. Things take time on all these things, but we make our own paths. I have really bad inherited cholesterol, so maybe I inherit one source of the problems that contribute, yet eating plant food since start of the year and I have the best cholesterol in 30 years+. So maybe things help and correlations are pretty good too. Maybe you inherit a whole bunch of other things and it isn't related to fats or foods for you but some other gene, or radon gas you were exposed to as a kid, or who knows? I don't, we just work with data as we see for ourselves.