Even if vaccinated people can contract the virus, they are likely to fight it off relatively quickly and keep the virus load in their bodes low, keeping their chances of transmitting it much lower than an unvaccinated person would.
Lets say being vaccinated halves your chances of passing on the virus compared to an unvaccinated person. If almost all the population get vaccinated, we can ease the lockdown to the point where we tolerate doubling the chances of re-infection. The lockdown easing and vaccination effect should cancel out. If vaccination reduces your chances of passing on the virus by 10x, then we can tolerate a 10x increased risk due to easing lockdown measures.
Worst case we may have to retain some limitations in social contact for a bit longer, but hopefully nowhere near as onerous or we've had to so far.
It may well be that having already been infected doesn't prevent you passing on the virus, in exactly the same way.
Whether your immune system knows how to fight the virus from previous infection, or from a vaccine, it can take time for your immune system to kick in and fight of a new infection. During that time you might be infectious.
Lets say being vaccinated halves your chances of passing on the virus compared to an unvaccinated person. If almost all the population get vaccinated, we can ease the lockdown to the point where we tolerate doubling the chances of re-infection. The lockdown easing and vaccination effect should cancel out. If vaccination reduces your chances of passing on the virus by 10x, then we can tolerate a 10x increased risk due to easing lockdown measures.
Worst case we may have to retain some limitations in social contact for a bit longer, but hopefully nowhere near as onerous or we've had to so far.