Yes, the physicist society really set back the public's understanding of ionizing radiation and its biological effects when they insisted on changing the units from the centimeter-gram-second system to the meter-kilogram-second system, and giving them all new names.
People don't realize how much radiation is given to them by medical procedures. And, the medical community seems to not consider the damage that their diagnostic practices can cause, not to mention their damage from some (illegal) events involving disabling safety systems intended to prevent overdoses or inadvertent doses.
For instance, I recently had surgery that necessitated scanning my skull multiple times. The problem was originally found with an MRI, which does not use ionizing radiation, but follow-ups were ordered with CAT scans, which give a dose of about 0.5 Gray (50 rads) to the exposed tissues. After 3 of those, I had to ask for a switch back to using the MRI, because a 4th CAT scan in that short time period would have reached the deterministic threshold of producing cataracts in my eyes within 8 years. If I had not spoken up, I would have had 2.5 Grays to my eyes by now, in a very short period.
Time period for delivery of the total dose is important when considering deterministic effects like cataracts, radiation sickness, and death. Probabilistic effects, such as cancer initiation, are considered time-independent with respect to how long the time period was when the dose was delivered, although there is a delay period used to associate the dose to the effects in data analysis. The difference is that the deterministic effects are considered to be caused by damage that the body can repair and recover from, while probabilistic effects at lower doses are considered to be damage to things like genetic material that cannot be repaired. However, the corneas of the eyes are biologically isolated systems with respect to fluid circulation, so repair is not expected there, and the dose that causes deterministic effects is therefore lower than in other tissues. So, for radiation to the head, the allowable doses are controlled by the eyes. For CAT scans to other areas of the body that do not expose the head to the radiation beam, the allowable total doses can be higher. And, spreading out the doses over time can allow for higher totals, as well.
Relating this to space travel, there is the concern that an event causing rapid dose delivery, such as being in the path of a solar flare emission, could quickly disable a crew of astronauts during their mission. However, the same dose over a multi-year mission would not have those deterministic effects. But, for both situations, the total dose would have some probability of causing delayed sicknesses or deaths years after the missions were completed. Those probabilistic effects are considered to have a probability that increases linearly with the total dose. That is often argued to not be true, but it is a reasonable approximation for computing risks to the astronauts in the dose ranges that are being considered.
As with medical decisions to use x-rays, the question for space travel is whether the potential gain is worth the risk. Determining both the risks and the benefits are not exact science, even though we try to compute numbers for some of the effects.