The initial error is their a priori assumption that science contradicts religion. A bad assumption and not at all a priori.
If a person believes that infection is caused by evil spirits, and not microscopic organisms, then yes, science very much contradicts their religion. What bothers me is when the people that believe in the evil spirit theory of disease insist that germ theory is atheistic because it contradicts their own religious beliefs, and insist that evil spirit theory is just as scientifically valid as germ theory.