Which specialists are best to diagnose and treat acid-base disorders like respiratory/metabolic acidosis and alkalosis ?

Since these kinds of disorders involve multiple organ systems, you probably want to begin with your primary care physician. Often, pulmonologists will deal with these problems in ICU patients and nephrologists will address severe metabolic abnormalities, but your general internist is likely capable of handling these issues and will refer as needed.

As a board certified internist and cardiologist you ask a great question. It depends on the doctor. This is basic medicine. Many primary care docs can diagnose this, or specialists such as kidney or lung doctors.