The very first mRNA vaccine was used a little over a year ago. You said, "the last I heard informally was that after about 6 months experience with a new vaccine, it's almost unheard of for serious side effects to show up." For that statement to carry any weight of persuasion, you must be referring to normal vaccines (with dead or sickened virus), so your statement only applies to the Johnson & Johnson vaccine. The mRNA vaccines (Pfizer, Moderna) are too new for us to be talking about side effects being unheard of.
Having said that, I don't see people wouldn't take the J&J vaccine.