There is no reason to think your immune system gets reprogrammed. Moderna and Pfizer type vaccines provide transient mRNA (UK and Russian DNA-based ones potentially could in theory make permanent modifications). It still has massive potential to go wrong, and the same tech was used for past influenza vaccines in trials where it was said to have uncertain safety profiles for widespread use. In the short term, massively bad immune reaction is possible, and no one is able to say about the long term because it hasn't been actually studied. I'd suspect many more subtle long term problems can arise.

Also, the material going into the vaccine is very easy to read by many labs. Something that reprogrammed or looked out of place would be noticed. It's not something that would be safe to create, unless you're assuming they could make a dangerous material that could be caught, but they'd be safe to ignore it.

But I'm sure that most Flu deaths will be blamed on COVID again, and probably only blamed on Democratic opponents.