The question raised by various people is "how radioactive are Mars/Moon rocks?" and as a supplemental, will there be consequences of living inside a building constructed from such rocks or excavated into the subsurface.

The answer is fairly straightforward, but will take a little time so brew a coffee and settle comfy in your chairs...

On Earth, radioactive rocks are mostly concentrated in the continental crust and especially concentrated in granites and some particular sediments. These rocks have specific origins that we understand and are mappable either by their physical appearance or simply using a geiger counter.

In some areas on Earth where these rocks are common such as granite belts, mildly dangerous amounts of natural radioactivity are found in houses due to choice of local building materials and seepage from the ground. The biggest danger comes from Radon gas and in our modern energy-efficient society this is made worse by having poor ventilation and recirculation of internal air.

Clearly, these issues will be relevant to a closed-cycle habitat on either the Moon or Mars. (No particulate filter can remove the radon).

As an aside, some types of modern plasterboard are also dangerous because they use a mix of minerals including plenty of potassium.

However, there is a good side. Both Mars and the Moon seem to have far smaller amounts of radiogenic isotopes in their crust than does the Earth, and in particular, neither body shows evidence of crustal recycling by plate tectonics (which is required to form granites), nor is there evidence for a long-lived ocean, which is required for most sedimentary deposits of radiogenic elements

Therefore, the most dangerous sorts of rock can be reasonably expected to be entirely absent on Mars and the Moon.

Even if they are not, a sensible choice of location and construction material for the habitat would eliminate most of the problems. For instance, we already have a map from orbit of the distribution of radioactive Thorium and Potassium on the surface of Mars.

One would ideally choose an area that was low in both materials, but also met the other requirements for a habitat.

Good areas include Hellas Basin and Hesperia Planum, Solis Planum, the plains SW of Elysium, and also those north of Olympus Mons.

Areas to avoid are the plains north of the Chryse outflow channels (Geological question - has something transported and concentrated radioactive material there?). Also bad are the alleged "lakes" south of Ma'adim Vallis and the lowland plains between Isidis and Elysium. Again, this may be telling us something about transport of materials.

I haven't yet seen a Uranium map, but on Earth this tends to behave similarly to Thorium.

I'm not a radiologist, but the basic physics suggests that it would be safer to be buried under 10+ metres of almost any regolith, rather than sunbathing on the surface.

The majority of the radiation exposure comes during the transit to/from Mars due to limited shielding in a low-mass capsule and long duration. Exposure on the surface of Mars, or the Moon is automatically half that in free space due to the excellent shielding under one's feet.

Remember also that the lifetime exposure limit is a highly conservative one, compared to other risks such astronauts face. Personally I'd accept 10 to 50 times the risk and still go to Mars.