I don't think there is any conclusive evidence on either side of this argument. For myself personally I only use moxabustion outside or in the clinic with heavily vented rooms. Do I think it is harmful? Not necessarily, but the whole more is better adage seemingly always comes back to hurt people. Now moxa clearly isn't tobacco, but it's also not a panacea for health either. I would think for peoples own safety, regardless of the evidence, moxa should only be used in treatment rooms with vents to the outside. We have one room in our clinic for moxibustion with a strong bathroom fan that vents outside and that seems to help. A disclaimer however, I don't use it extensively, but give it to patients to use at their home as self-treatment quite often - and tell them to use it outside if at all possible. More for the smell than a risk to their lungs per se, but it's probably safer outside anyhow.
Certainly many practitioners use lots of moxa for years and don't have problems, seemingly at least. But I have seen it aggravate practitioners with underlying lung problems like asthma, etc. so from that it appears it's not without any inflammatory risk.
Certainly there are studies like, Cytotoxicity and Radical Modulating Activity of Moxa Smoke, that have shown anti-cancer properties of moxabustion smoke. Then a meta analysis and analysis published in the British Medical Journal that tried to answer "Does The Burning Of Moxa Constitute A Health Hazard" and they found the following:
"Results: Levels of only two volatiles produced were equivalent or greater than the safe exposure levels, as was the carbon monoxide level reported, both as a consequence of using worst case assumptions for comparison. Under normal operating conditions neither volatile nor carbon monoxide would present a safety hazard. One group of chemicals tested, the aromatic amines, with known carcinogenic properties have no agreed safety levels. Results for these in the study compared favourably with background levels reported in urban environments.
Conclusion: There are no immediate concerns arising from the continued use of moxa as a therapeutic modality in traditional Chinese medicine. Further testing may be required to establish whether current recommendations for ventilation and cleansing of treatment room surfaces may need to be revised. Stronger recommendations may also be necessary on the inadvisability of using moxa on broken skin."
So from that I would say concerns are low overall, but ventilation probably isn't a bad idea.