I personally think reinfection happens all the time. No matter if you are vaccinated or had the disease, if you are exposed to a heavy viral load, it's going to be a while before your immune system manages to kill all the virions. When you are exposed to a small load, that infection time may be minutes. Immunologists talk about a "sterilizing vaccine", which means the vaccine is so effective that any virus is immediately attacked and you never do shed enough to pass it to anybody else. The Covid vaccines are not that effective. Very few vaccines are.
You have to be shedding enough virions to infect anyone else. When they test people by PCR, they talk about CT counts which are the number of cycles they need to double the RNA from the swab before it can be detected. If they have to double it 40 times to get a positive, you will infect nobody. People with a full blown infection have CTs of 10 or less. That's billions of virions they are shedding.
So I think a vaxxed person CAN be infected, but very likely will be asymptomatic and not contagious. That's why CDC said vaccinated people can socialize with other vaccinated people without masks. But I would not want to have close contact with anybody unvaccinated without masks: You could get enough of a viral load to carry it home to some unvaccinated person and make them sick or even dead, even though you remain asymptomatic.
On a different topic: When Long Covid victims get vaccinated, about half of them feel a lot better after about two weeks. There are currently two theories as to what's going on.
1) Their immune system is in disregulation. When they get the vaccine, their immune system goes into "war mode" and then after all the vaccine antigen is dismantled, it goes into the normal "system reset" mode. Kind of like unplugging your computer and then plugging it back in when it is hung up.
2) Corona viruses are gut residents in bats, and cause no illness. In humans with Long Covid, the viruses remain infecting the gut for the long term without stimulating a full blown immune response. (We tolerate a lot of foreign antigens in our guts.) The vaccination makes enough antibodies to wipe out those gut viruses.
There is some evidence for both theories! We know Long Covid victims have disregulated immune systems. And researchers found viral RNA in fecal swabs long after normal nasal swab tests went negative.