I appreciate concerns about possible unknown side-effects of the vaccine. But that should also be balanced by both known and unknown side-effects of covid-19 itself.
That is, if you’re concerned that vaccine side-effects might pop up in 10 years, then you should be equally concerned that covid-19 side-effects will also pop up in 10 years.
If you choose not to get the vaccine because of that concern, then you’re essentially choosing to take the covid-19 risk instead.
That said, it is well-known that covid-19 has a significant risk of medium-term side effects, e.g. the long-haulers. In fact it’s unknown how long the long-haulers may be affected; it may well be lifelong. There’s also known long-term side effects such as diminished lung capacity.
I’m unaware of serious medium-term side effects from the vaccine; there’s the blood-clotting thing, but I believe that’s literally a one in a million side-effect. If there’s serious issues that can last for months, I’d be interested in hearing about it.
So I don’t think vaccinated people are ignoring unknown vaccine risks or playing them down. Rather they’re looking at the well-documented covid risks and wondering why people think getting covid is safer than a vaccine. Some people fear the unknown more than the known, and some are the opposite.