"fully vaccinated individuals with breakthrough infections have peak viral load similar to unvaccinated cases and can efficiently transmit infection in household settings, including to fully vaccinated contacts." [1]
[1] https://www.thelancet.com/journals/laninf/article/PIIS1473-3...
Vaccinated people are less likely to be infected, hence "breakthrough case." Your quote is like saying that "people thrown out of windows in car crashes have the same rate of injury, despite whether the person was wearing a seatbelt or not." That may be true, but wearing a seatbelt definitely reduces the chance of getting thrown out of a window.
a) choose the later study
b) look at what happens in the real world (e.g. https://news.ycombinator.com/item?id=29124652 )
And, If there is uncertainty (and there always is some small amount of it) then this does not support the parent commenter's strong and confident assertion that "do not, and never have" ... produced an effect.
b) in the real world, we had our biggest outbreak after vaccines were mainstream
Is that supposed to be relevant? When "we had our biggest outbreak" there were/are still sufficient unvaccinated people to transmit an outbreak.
You're clearly defending a fixed point of view here. If you want detailed responses to learn from, stop asking for people to do them yet again and look for what already exists upthread. If you're having trouble finding it, start here: https://news.ycombinator.com/item?id=29124446
If none of these seem to suggest a clear winner then you should just think that this is still undecided. You can also ask an expert. Choosing one and believing is basically just going with your suspicion.
Based on this study, vaccinated had a 25% chance vs 38% for unvaccinated to become infected if someone in their household had Covid. So a helpful reduction, but not night and day.
Once infected, from what I’ve read vaccinated folks are just as likely to spread it.