60 microseverts an hour works out to about 525 millisieverts (mSv) per year. The general public limit is set very low, so for additional reference, the annual limit for emergency worker was raised to 250 mSv per year after Fukushima, half of what you'd get on the Moon. An effective dose (whole body, sum of all equivalent doses for the organs) of 200 mSv is enough to increase your risk of fatal cancer from 25% to 26%, so 525 mSv obviously represents a substantial stochastic risk.
The ICRP occupational equivalent dose limit for hands, feet and skin are 500 mSv per year, so for these you're under the limit (the 525 mSv effective dose above is spread across you, not on one organ). However the equivalent dose limit for eyes is 20 mSv average with no more than 50 mSv per year. I haven't done the math but I think 525 mSv effective dose over a year would put you at substantial risk of deterministic damage to the lenses of your eyes.
In other words, Moon men probably get cataracts and are more likely to die of cancer.
The ICRP occupational equivalent dose limit for hands, feet and skin are 500 mSv per year, so for these you're under the limit (the 525 mSv effective dose above is spread across you, not on one organ). However the equivalent dose limit for eyes is 20 mSv average with no more than 50 mSv per year. I haven't done the math but I think 525 mSv effective dose over a year would put you at substantial risk of deterministic damage to the lenses of your eyes.
In other words, Moon men probably get cataracts and are more likely to die of cancer.