As adjectives the difference between dogmatic and religious
is that
dogmatic is (philosophy|medicine) adhering only to principles which are true
a priori , rather than truths based on evidence or deduction while
religious is concerning religion.
As nouns the difference between dogmatic and religious
is that
dogmatic is one of an ancient sect of physicians who went by general principles; opposed to the empiric while
religious is a member of a religious order, ie a monk or nun.