So much so that the first humans, Apollo 8, didn't even mention these belts anywhere in the transcripts or reports.
Really?
From the Apollo 8 transcript;
Apollo Control here. And we're 5 hours, 9 minutes into the flight and we, as you heard the crew record, the S-IVB is doing its propulsive vent. Now we should see a pretty dramatic separation between the two vehicles. The S-IVB will remain on a path which will take it essentially, if you consider the Moon straight ahead of you for analogy purposes, it will take the S-IVB to the right of the Moon while the spacecraft will veer into the left and slightly ahead of the Moon. Earlier in that conversation you heard Anders reporting his PRD readings. That's the Personal Radiation Dosimeter, and perhaps another dosimeter and they were down on the negligible range as we anticipated they'd be, although the crew at this point has passed through probably the thickest portion of the
van Allen radiation belt as it departs the Earth. It'll continue to go through some residual background radiation on out to about 40,000 miles. The - That's the new position in this flight, the flight controller named radiation has been instituted because of our passage through the
belt. And at this point we've heard nothing from him which is about what we expected to do. At 5 hours, 10 minutes into the flight; this is Apollo Control, Houston.
Over the next few hours, Frank Borman would get increasingly unwell, with some concern amongst the doctors on the ground that it was from radiation, or the Asian Flu. Today, Borman's sickness is attributed to Space Adaption Syndrome.