In some proportion of hospitals, when someone who is not vaccinated goes to hospital for any reason, they are tested for COVID-19. If found positive this is counted as a COVID-19 hospitalization. We have no access to the precise rate of these incidental hospitalizations. In some of these hospitals, it is the policy that vaccinated people who go to the hospital are NOT routinely tested unless they have symptoms. If this is the policy at a substantial number of hospitals, it could dramatically change the "effect size" of the measurements that we are talking about. The same issues essentially applies to COVID-19 deaths and cases.
Large effect size alone generally isn't convincing when you're using such fundamentally confounded sampling procedures, merged age-groups with wildly different risk profiles, and data aggregated across long time-windows with different population sizes.
It's not a conspiracy, people just tend to look away from things that could endanger their livelihoods. An emergent property of socioeconomic systems. A failure mode, so to speak.
The effect of the vaccines is so huge that you only have to look at a Kaplan-Meier plot and will immediately see the huge difference. And we don't have a single study here, we have a lot of different ones that all indicate that the vaccines are very effective and safe.