Lunar dust is scary stuff from a human health perspective. It's largely made of microscopic rock fragments from meteorite impacts. Because there's no weathering on the Moon it stays sharp for billions of years. It's one of the reasons I'm wary of crewed lunar bases.
Mars is actually far safer from a dust perspective. Because there is an atmosphere (even if a thin one) meteorite dust weather's away into safer, rounder forms.
Yeah that dust is definitely going to be a problem from what I understand. Although, dust on Mars isn't that much better from what I've read. It doesn't have the sharp edges, but it is extremely fine and will get in the blood stream. So, hard to say what the long term effects of that would be.
One of the interesting Mars base concepts I've read is to equip airlocks with a combination water shower/positive air pressure system. When an astronaut returns, they stay in the airlock with the outer door still open, and the airlock continuously blows compressed Mars air towards the outer door to prevent dust from being blown inwards by natural winds. At the same time, the still-in-a-spacesuit astronaut takes a shower to wash most of the suit dust off. Mars has the advantage of mass quantities of water easily accessible across most of the planet in the form of subsurface ice. For example there's a glacier just a few metres under the surface of the area known as Utopia Planitia with at least as much water ice as Lake Superior here on Earth. The shower/forced-air system would be relatively straightforward by space engineering standards. it's just some plumbing and air compressors and making sure that the water deluge isn't a problem for spacesuit or base electronics. The air is completely harmless to any equipment we'd send. It's mostly CO₂ with a bit of nitrogen, argon, and traces of other safe gases.
This kind of system sadly isn't practical for the Moon because there's no air, and there's basically no water outside of the permanently-shadowed polar craters. It'd be a big waste of scarce resources that would be needed to be shipped from Earth at great expense. There's some concepts involving electrostatic repulsion but it's going to be a big engineering challenge to make it work in practice. I'd sooner bet on extensive use of telerobotics on lunar bases for most work, with the crew staying inside except for rare situations that require their in-person attention.
If the Moon weren't so close to us we probably wouldn't give it a second thought for crewed exploration missions. From a human health perspective, it's one of the worst places in the solar system with a solid surface. I've often thought that we should reserve the far side for science (especially radio astronomy), the near side for industry where it doesn't matter how much toxic waste is produced because there's literally nothing for it to kill no matter how improperly stored, and leave exploration to robots.