There is no doubt that massage and it's related therapies can be of benefit, often great benefit. And any chiropractor is required by law, I believe, to refer patients to MDs at need. The flaw in chiropractic is that it operates according to theories that are unproved or disproved. Also, some trends in chiropractic, such as manipulations for the very young, have proved to be dangerous. Allopathic physicians normally practice under some form of peer overview, especially if they want to keep their hospital privileges. Others seldom do. That is their greatest weakness and greatest danger.
You seem to mistake the scientific method for ideology. That is a misunderstanding. The "scientific method" a la Poppers, etc., is a description of the techniques that have given us the things that help make life worth living. When something claims to be "scientific" but is unable to meet the minimal standards of the scientific method, then it ain't science.
Let me invite an onslaught by adding clinical psychology to the list. It ain't science.