With the tat thing, I do think that there are several relevant points about that. One is where you live, and that seems to matter a lot. Where I grew up in PA it seems everyone has one and no one cares no matter the type of job you are doing, professional or not. Where I live in Utah now, a fair number of people have them but they are not so commonly accepted which I believe is probably for two reasons. There is a strong Mormon population here and there is also a focus on professional work rather than the manufacturing that is where I grew up. Here I would be expected to cover a tat up, and I know that and accept it. I think the reason my husband is also resistant to it is because we are Mormon, although he grew up that way and I didn't which is why my attitude is more meh... it isn't a big deal, it is for a real medical reason and whatever dude. And his attitude is zomg you'd be defiling your body! I think the point about it the worker and the Jewish nursing home was also a good one. Everything is about context.
As a general rule, we like to think our medical records are all digitized now. And sure, I can walk into the records office of any of the affiliated hospitals around here and get all of my records from every hospital and doctor's office but... Hah, you knew there was a but right? I still have to explain to every person every time I get to the hospital, a new doctor's office, ER, even if it is the same ER I've been to a few dozen times, what my allergies are. These include penicillin and latex so you would think that they are glaringly obvious and all over my digital chart in some sort of way that can't be missed right? Nope. Going for a blood draw? The first words out of my mouth have to be that I have a latex allergy. They don't check, and they don't ask. Our digital medical records are useless to us as protection when it comes to our allergies or even celiac. Mine also state with my celiac, because I made them put it in the allergy section that I absolutely can not be given oral medication under any circumstances. I doubt they'll pay attention to that when they decide they want to try to force something on me.
If you think your son will feel better if you have a bracelet, go for it. Especially if he hounds you about it.