Judging by current evidence, vaccines continue to provide strong protection, about 90%, against death or hospitalization, for many months. Protection against infection is much weaker. A recent study in Qatar found that the Pfizer vaccine's protection against infection got down to about 20% by the fifth month. That is the lowest figure I have seen; other estimates of the effectiveness of vaccination against infection over time vary, but 50% is fairly typical.
If the question is whether I should get vaccinated in order to protect myself, the main issue is effectiveness against hospitalization or death. If the issue is whether you should get vaccinated to protect me and others, on the other hand, the main issue is by how much vaccination reduces the chance you will get infected and be contagious.
People are likely to take fewer precautions against getting infected after they are vaccinated — certainly I did. If effectiveness is down to 20%, even 50%, the chance of infection might easily be as high among the vaccinated as the unvaccinated. Infection of the vaccinated is more likely to be asymptomatic, in which case the individual is unlikely to know he is infected, hence unlikely to take precautions against transmitting the infection, which increases the chance of transmission. It is, so far as I can tell, unclear how close the relation is between severity of infection and contagiousness — at least I have seen claims both that asymptomatic people are much less contagious and that they are not.
I conclude that while it is clear that by getting vaccinated I protect myself against consequences of Covid, it is not clear, contrary to what the CDC, Biden, and a lot of other people claim, whether and how much I protect other people against the risk of my catching Covid and passing it on to them. It is that claim on which the current push to require people to be vaccinated is based.
Some evidence that while vaccination may reduce contagion it doesn't reduce it very much is the lack of any clear connection in international data between vaccination rate and infection rate. Israel had steeply increasing infection rates from late June to early September, the UK from late May to late July, periods in which both had relatively high vaccination rates — higher than Czechia, which had declining rates until late June, roughly constant for the next two months, and much higher than India, which has had a declining infection rate from early May to the present. I have not yet seen any careful analysis of the international data trying to separate the effects of climate, vaccination rate, and natural immunity from previous infection, but the effect of vaccination alone is not large enough to be obvious from a casual look at the data.