Nobody knows yet if it's an issue or not. For all we know, it could be healthier than full g. Or it could be nearly as bad for us as zero g.
There are simple experiments we could do to find out. If anyone is ever serious about this, perhaps they can do these experiments, using a tether based "artificial gravity lab" in space. We could have done this any time from the 1970s onwards but it's just never been done.
If we do need artificial gravity on the Moon - then that could take two forms, depending on the "gravity prescription" and human tolerances of spin.
If we can make do with say an hour or so of gravity a day - then that could be done in a short arm centrifuge spinning at say 30 rpm. Or if we can tolerate high spin rates - could use similar methods e.g. for entire night while sleeping, while eating meals etc.
Or else - if the gravity has to be present all day and all night for health - and if it turns out that humans just can't acclimatize to the spinning motion - then the entire habitat needs to be spinning - and pretty huge. Or else - another idea that[s been suggested - is to have the habitat as a train that is continually moving around a circular track on the Moon at right speed to generate 1 g outwards artificial gravity.
BTW - some people have damaged vestibular systems in their ears and can't detect and aren't affected by spinning motions and giddiness. In all other respects are normal and may well be able to be good astronauts.
They could be healthy in even small habitats using high spin rate short arm centrifuges at say 30 rpm.
Someone like that would almost certainly not need anything more than a small short arm centrifuge to keep them healthy long term in space. Perhaps they might be the best people to send on long multi-year interplanetary voyages since they can make do with such small spaceships...
Or you could have artificial gravity habitats in space - easier to construct - just two habs connected to each other by a long tether - and then control telerobots on the surface - e.g. from L1 or L2 positions or both.
In any case humans on the Moon would not spend much time in spacesuits or on the surface - because who wants to increase your lifetime risk of cancer? No known effective way of protecting spacesuits - or lighweight rovers - from cosmic radiation.
So - they might as well be in an orbital facility as in a cave on the ground, if they need artificial gravity to stay healthy and need it long term 24/7.
But - this is all total speculation. Nobody has yet done the experiment. So the only answer can be - that we don't know.
We surely need a better system than the ISS - so - able to live their long term for years on end - and also - able to provide their own food and reasonably closed system habitat.
Otherwise would be an immensely expensive business just keeping them supplied from Earth and rotating people to and from the habitat - which if you followed the ISS model you'd need to do every few months.
Perhaps the ISS model is the only one that works in space. But nobody has tried anything else or done the basic experiments needed to see if artificial gravity and closed system habitats might work better. And there are indications at least that if enough work and research was put into this - with experiments in space not just on the Earth - that it might solve some - and maybe nearly all - the health and supply issues in the ISS - and make long term stays in space far less expensive and easier to do.
You might like my article on a suggestion by Joe Carroll for an easy way to get our first data about this, and another idea for a way to test to see if a short exposure to artificial gravity for an hour or so a day helps inside of the ISS using small centrifuges.