So far the studies that appear to show a correlation between meat consumption and negative health outcomes have all been barely a step above junk science. We're talking about observational studies with poor controls (healthy subject effect), multiple uncontrolled variables, and small effect sizes.
I would say that the evidence on red and processed meat and CVD and CRC is at least a “B”, so we’re meeting your goalposts here.
When we look at the totality of the evidence via meta analysis, we see effect sizes in the 10-20% range for IHD. If 20% change in one of the leading killers in the western world is “small” to you then fair enough, but I’d suspect that’s a fairly proprietary use of the word that wouldn’t accord with what most people mean when they use it.
I’m not sure what variables you think are uncontrolled in these studies, you’ll have to be specific about which uncontrolled variables you think are having an effect.