Nope. No, "they" don't. Who's "they," Clete? The study was comparing the efficacy of cloth masks and medical masks used by healthcare workers in hospitals in Vietnam. The control group is clearly stated:
Intervention
Hospital wards were randomised to: medical masks, cloth masks or a control group (usual practice, which included mask wearing).
I myself choose to use a medical mask, because I'm able to afford to buy a box of medical masks and discard them. Many people here and around the world do not have that ability or perhaps they may prefer cloth. Even among cloth masks there's variability - between materials, number of layers, whether there's filter material in the layers, how they're sanitized, etc. But for those who wear cloth masks:
Conclusions
This study is the first RCT of cloth masks, and the results caution against the use of cloth masks. This is an important finding to inform occupational health and safety. Moisture retention, reuse of cloth masks and poor filtration may result in increased risk of infection. Further research is needed to inform the widespread use of cloth masks globally. However, as a precautionary measure, cloth masks should not be recommended for HCWs, particularly in high-risk situations, and guidelines need to be updated.
Most likely we all agree our medical professionals should be wearing medical masks or better. Unfortunately many of them were forced to use even medical grade protection in ways they weren't intended - repeated uses when they were supposed to have been discarded between patients or between shifts. But what exactly is the intent of the OP? Drop a pile of links purporting that wearing masks is bad for you? Compared to what, exactly? Do medical professionals endure the bruises and broken skin in order to better protect themselves against infection? If the OP was making an honest plea for people to choose medical masks over cloth masks, I could understand that. It's pretty clear medical masks are better. But do cloth masks help at all, even a little, if nothing else as a reminder not to touch one's face when running to the store in suburban U.S.? If you live in rural Vietnam, perhaps better guidelines on how to wear cloth masks when medical grade masks aren't even an option?
Anti-maskers simply don't want to wear a mask, and they don't want you to wear a mask.
"Covid overlords"
Okaaaay....