In my fictional universe, people have colonized a planet that orbits an F-class star. I know these stars give more intense radiation and solar flares than G-class stars. This leads me to think bunkers or underground structures may be needed to protect colonists from higher radiation. But is this necessary given that the planet has a strong magnetic field? Am I over-anticipating the radiation?
If your F-class star is stable (not a variable star) then your primary problem is the much higher proportion of ultra-violet in its output than our Sun. This is an inevitable result of its higher temperature, which also means it will have a shorter life than Sol.
It seems that if a planet is at a comfortable distance from an F-class star as regards temperature, it will receive somewhere between 2.5 and 7.1 times as much UV. The exact figure depends on the distance between the planet and the star, and the temperature of the star within the F0-F9 range.
To counter this and produce a "shirtsleeve" environment, you're going to need your planet to have a deeper and/or denser atmosphere, which means higher atmospheric pressure. This will be reasonably plausible with an F8 or F9 star, a planet far enough away from it to be a bit cooler than Earth, and an atmospheric pressure about twice that of Earth, with a lower proportion of oxygen. If you can manage all those things, you won't need shelters, but the inhabitants will need to be pretty cautious about UV exposure, unless they have high melanin levels.
If you are in habitable distance the only problem will be a higher amount of UV radiation.
On Earth the ozone layer protects against UV radiation. So you will want to have more ozone in the upper atmosphere or another gas that does the job as well (if there is one).
You do not need a thick atmosphere. What counts is the composition of the atmosphere. (a higher atmospheric pressure could have worse health effects than UV light).