There is certainly a lot of difference between ID and immunology but you would expect a lot of overlap given how the symptoms of allergy can mask or be essentially identical to pathogenic infection. DOs are sometimes viewed as a little flakey as their practice includes “osteopathic manipulative medicine” (essentially chiropractic manipulation albeit generally without the woo) but their basic medical school education is essentially the same as an MD except for a larger focus on preventative medicine, and their board certifications are essentially identical between ABMS and AOA specialties. I think in practice the difference between the basic training and capability of a MD and DO in a certified specialty is less than the difference between individual physicians.
If your doctor has helped with your asthma, then it sounds like he’s at least a good allergist. I just wouldn’t take his opinions about vaccination with a lot of credibility in absence of a second opinion or some clear evidence.
Yeah, doctors are trained and often actively cultivate an air of authoritative infallibility even though they are just human beings with the same propensity toward personal bias and irrational belief as everyone else. I’ve met some physicians with pretty off the wall notions, and of course neurosurgeon and former Secretary of Housing and Urban Development Ben Carson was fully of nuttery as I noted previously: