The prejudice is based on their ignorance of science. In fact, traditionally, chiropractics totally eschews science in exchange for philosophy. This leads to chiropractors using techniques that have been shown to be harmful, such as doing spinal manipulation to fix nerve impingement, which is contraindicated by numerous studies. Additionally, there are still many chiropractors that are anti-immunization, another scientifically baseless position, but one that is dangerous for both the individual and society.
Insurance coverage is not an endorsement whatsoever. It is the effect of heavy lobbying on the part of chiropractors. Remember, insurance is not incentivized to do what is best for the patient.