First of all, no I am not a doctor and never claimed to be one. The MD in my screen name stands for Maryland as in “Maryland Expat In Pennsylvania”. Next, you are the one who does not understand how vaccinations work.
When a person is properly vaccinated, the vaccine stops the illness before it starts, and even when those who are vaccinated are exposed to the disease, they will either not be contagious at all or will be so for a much shorter time and generally with a milder form of the disease.
In other words, an immunized health care worker is just as likely to spread a virus. And I seriously doubt that a health care worker with Rubella or Pertussis would be "on the job".
Wrong. Immunized people are very much less likely to spread a virus for which they have been vaccinated for. This is why Herd Immunity works to some extent; if enough people are, people who are not vaccinated and those who have been vaccinated but have not yet reached full immunity are somewhat more protected. Also consider that with many diseases, the infected person can transmit the disease before they themselves become symptomatic or sick enough to stay home.
If by stopping the illness, you mean stopping the manifestation of symptoms from the infection, that is correct.
and even when those who are vaccinated are exposed to the disease, they will either not be contagious at all or will be so for a much shorter time and generally with a milder form of the disease.
That is conventional myth. A vaccination only increases immunity in the recipient. It does NOT create some magic barrier that prevents the virus from entering a host or likewise prevent the virus from being transferred from host to host.
If you believe otherwise, then I guess you believe it's not necessary for health care workers to practice hand hygiene, since once they're vaccinated they no longer are contagious. Is that your contention?