Right now, the only absolute medical contra-indications for the mRNA vaccines are a previous anaphylaxis to the vaccine or one of the components.... and kids, but that will likely change once the trial results come out. Active treatment with chemotherapy is also not a contra-indication, although this might diminish the efficacy of the vaccine. So, we're talking about a really tiny percentage of the population that has true medical reason why they can't receive either the Pfizer or Moderna vaccines.
I'll need to check specifically on Johnson & Johnson, but I'm pretty sure the same applies to their product.