Within the realm of theology there are several subsets, Christology, Pneumatology, Anthropology, Hamartiology Soteriology, Angelology, and Eschatology.
All that is theology comes directly from the Bible, there is no other source. This is why the oldest rule of hermeneutics is:
Quod non est Biblicum, non est Theologicum
i.e. If the quote is not from the Bible, it is not theology.
Doctrine comes from the Latin doctrina which means to teach. These are the beliefs one derives from theology. (e.g. The word “Trinity” is doctrine and not theology.)
Dogma are the principles that a group operates under. In Christianity this come down to morals and behaviors, things like how one is baptized, what constitutes communion, and how traditions and holidays are to be observed. The dogma cannot be changed without changing the groups doctrine.
As Messianics we are often called heretics because our theology does not match some other group’s dogmas. They have chosen to denounce us, in order to justify what they are doing, as they have no theology to back their dogma. Many feel a need to hold on to one or more dogmas at all cost. This is because the dogma unbeknownst to them, has become the object of their worship. They simple cannot see their faith being valid without these practices.