At worst it can do worse than nothing.
For a big chunk of the population vaccinating is very safe because the virus is very dangerous. A vaccine doesn’t have to be very safe for a disease that kills on the order of one in a thousand off otherwise healthy adults.
Being very young or already having contracted the virus significantly alters it’s risk profile. With a virus several orders of magnitude less deadly you have to start being much more careful that the vaccine is provably considerably safer than doing nothing. That’s not hard when you’re trying to beat 1 in 1000. It is very hard when you’re trying to beat a one in millions risk.
There have been concerns and side effects. Much less amplitude in signal compared to the virus, but still big enough to halt briefly a few of the vaccines, still enough that small children don’t get emergency authorization, still enough for a few warnings about immune reactions.
It is very rational to take a one in a million risk to prevent a one in a thousand risk. It is very rational to pause before taking a one in a million risk that could very well prevent nothing.