I think people who are at risk of having anaphylaxis from the mRNA vaccines probably should get a different vaccine. Anaphylaxis is extremely serious. Just because you are being monitored doesn’t mean you won’t die. The severity of the risk when anaphylaxis occurs doesn’t need to be handwaved in order to say that people should still get vaccinated. There may be a very small number of people who are at higher risk of anaphylaxis plus a contraindication for other vaccines. I would leave it to them and their doctors to figure out whether any vaccine is advisable, balancing the risks of getting covid while unvaccinated.
That said, I think licensing authorities should go after, and if applicable criminal charges should be brought against, any doctor who is providing made-up excuses for people who are just anti-vaccination.