As it turns out, most psychedelics have anti-inflammatory and immunomodulatory properties. This is a pretty good literature review on the subject.
Long story short, activation of the 5-HT2A serotonin receptor by psychedelics in a functionally selective manner blocks the effects of TNF-alpha, reducing the gene expression of IL-6, IL-1beta, and others important to inflammatory processes. Some psychedelics may have other mechanisms which peripherally reduce inflammation - for instance, in addition to its serotonergic effects, LSD is a dopamine agonist, which has some overlap with drugs like pramipexole which have been used to treat fibromyalgia, and Abilify (aripiprazole), which has been used for ME/CFS.
One interesting thing noted in the literature review is that the phenethylamine psychedelic DOI (2,5-dimethoxy-4-iodoamphetamine) had anti-inflammatory effects that were an order of magnitude more potent than the other psychedelics tested. Perhaps microdosing DOI would be ideal for producing therapeutic effects without an actual trip. However, DOI would probably be very difficult for the layperson to acquire compared to more popular psychedelics like LSD or psilocybin mushrooms.
Back in the day, I used to do psychedelics quite often, and I felt like they've had a net positive effect on my life, especially my life philosophy or mindset. Sometimes I wonder if I might have gotten ME/CFS or autoimmune SFN sooner had I not done taken these drugs. I stopped using them regularly a couple years before my ME/CFS onset, because their gastrointestinal side effects really made it difficult to enjoy or make use of the trip (at the time my IBS was worsening dramatically). Unfortunately, I feel like my ME/CFS and GI problems are too severe currently to realistically try psychedelics, even microdosing.
Even in mild or moderate ME/CFS, I would worry that using psychedelics would provoke an episode of PEM. In my experience, microdosing LSD was very mentally stimulating, akin to taking a small dose of amphetamine but with fewer physical side effects. Mental stimulation can be fatiguing, and it's not so easy to 'stop' drug-induced mental stimulation the way you can turn off an exciting movie. At the very least, it would be wise to have some kind of sedative on hand in case PEM started to occur. A single dose of benzodiazepine would probably work okay for this purpose. I've read trazodone is excellent at 'killing' a trip, since it is a 5-HT2A antagonist, but even though I take trazodone these days, I've never had a chance to use it to end a trip.