(Ninjaed, while I scrawled the following.)
Chance of catching the virus when vaccinated < Chance of catching the virus when unvaccinated
(On being exposed, the naive body is never less likely to succumb than an informed version of the same body... And I'm discounting equal likelihood as tied up in the same issues as would make a vaccine as dangerous/ineffective in a very small proportion of cases that should be medically known in advance.)
Chances of passing on a virus caught while vaccinated <?/?> Chances of passing on a virus caught while unvaccinated.
(An unknown, but as subordinate probability within the proportional 'caught' chance below the 'exposure' chance it would need a very detectable uptick in onward transmissability in a vaccinated case, from a baseline low transmissability from natural and unprepared-for infection, to overturn the above. And if either were true then we'd see signs. Or even, in the case of the latter, there wouldn't have been a pandemic to see signs of. And, before anyone mentions it, you don't get "shedding" with any of the usual range of vaccines we're dealing with here.)
Chances of people oversocialising, given vaccinated vs. unvaccinated status, and allowing the pure per-exposure chances to be repeated at a high enough rate to outcompete the other status...? That's the question. Even if everybody is totally unvaccinated, if they never get exposed then they can't catch it. But then we know that at the 'height' of lockdowns people were still catching it, so people were never hermetically isolated that much. Post-lockdowns (v1) and pre-vaccine, people caught the thing even more, hence any repeat lockdowns/precautions asked of them. Post-vaccine, the further upblips occured in the young and unvaccinated, though whether that was because of youth (intrinsically less troubled to avoid risks, or more likely forgo the common sense the politicians insisted could replace hard-nosed legislative isolation measures) or vaccination (the lack of lowered catch-chance) or whatever mixture of the two, I don't have figures to say.
Needless to say, if the 27 vaccinated people now insist on greeting each other and all those they socialise with in the wider world with a mutual forced cough into each others' mouths, whilst the 28th and unvaccinated individual goes to work (and everywhere else!) in an Apollo spacesuit with its own launchpad-type air supply, then we know that the problem (at least all the problem that does not include use of space-nappies) is firmly upon the vaccinated.
In fact, with a pool of 27, it makes breakthrough proportionately more likely (at first contact) in that group. 99% protection (per individual) means 76% protection (for the whole group); 95% -> 25%; it quickly becomes all-but-certain as we try lower baseline unsusceptibilities for that group. But then the other 26 are still individually less likely to catch/propogate, and the 1 with 'background immunity' is still more individually vulnerable, either to catch from the unlucky group member(s) or to be the one to test their luck.
And, in an individual exempt from vaccination on medical grounds, perhaps they'd be taking special care. Vountarily distancing, in the office, masking, etc - or even arranging to work from home - while not congregating with others (especially not others like him) in social situations beyond/between the working hours.
But someone who chooses not to, I'll go out on a limb and say they regularly meet up with fellow no-vaxx-no-mask-no-way-no-how types, increasing their risk more than even with random encounters with maybe-vaxxed-maybe-not people.
I'd say that vaccination is not the be-all-and-end-all of protection. One must still be wary as you trust to the general wariness of others[1], but it helps, both you and those you inevitably come in contact with, and more so if they have tried to be so helpful too. You need to have better reasons to actively avoid vaccination than to consider the risks of careless vaccinated people to be higher than (or even nearly as high as) those of heedless unvaccinated ones. And we can discuss those 'better' reasons, of course.
[1] Last weekend, I met up with someone I hadn't seen for two years. Don't know him well, it was just at a place we had both been, and had last been at that self-same full two years ago, for the same purpose, and done some mutual task together with, that (skipping a year) we were now back again to do. He extended his hand to shake and I hesitated a moment but ultimately reached out to complete the gesture. I could feel my thoughts trying to balance the potentials (like a positronic brain balancing a very strong 2nd-Law command vs a vague and uncertain issue with 1st-Law imications) and it made me uncomfortable. I don't think he noticed. And I never asked him if he was vaccinated (nor discussed the issue). But, for both our sakes, I would probably have defaulted to a polite refusal, tempered with a joke, had I been not so certainly vaccinated in my mind. Using my long prior history of being an asocial introvert, even during the time when the only mask I ever needed was my fake-sincere smile that apparently also reaches up to my eyes. Am I now more at risk for having risk-shifted on the assumption of my vaccination being sufficient? More than a vaccinated-refusal, less than an unvaccinated-acquiescence... I would say also less than an unvaccinated refusal, too, so long as hand-hygiene is not severly lacking, given it's an airborne issue more than a bodily contact one, but I'm (once more) still not an habitually tactile person so I'd say this is a very minor vector compared to any airway carelessness I might succumb to by mere unmasked/mismasked proximity, even in the cold (overcast) light of the outdoors, downwind of who-knows-who. To analyse my own circumstances as objectively as possible.