I was once told that watches are unlikely to set off metal detectors. Mine has a leather band but plenty of metal on it (it's a Tissot.) I take it off if I'm not in PreCheck line. The PreCheck machines are calibrated at a reasonable setting.
My ring is too hard to take on and off, but I don't think that a gold band is as likely to set anything off. It's not a terribly glamorous ring.
The worst was being told that I had to take my eyeglasses off. They're onobtrusive, mostly plastic. That was in Cincinnati when the TSA first started.