Should theology be a recognized field of study in universities and other publicly recognized and accredited educational institutes?
As far as I am aware, universities offer bachelor degrees in Theology and Religious studies. Of course they are recognised as a degree, but generally the scope of their influence remains restricted to the particular church or religion they are based upon.
Why? There is nothing in theology that can be objectively studied and tested like the sciences. There are degrees in fields other than science; literature, history, the arts. Is theology like them?
Theology is not so much about objective studying and testing of particular concepts, rather it provides a more advanced insight into the religion itself, or more often, its scriptures. For example, Christian Theology courses mostly consist of advanced Bible study. I disagree that there is nothing in theology that can be objectively studied, as there are many different interpretations of the scriptures that may be compared and opinions on certain occurences may differ.
Why are there not degree programs in astrology, alchemy and numerology?
Most likely because such courses would be unprofitable. Just as theology courses differ according to that countries most practiced religion - Islamic theology is taught in eastern nations, Christian theology in western nations - other such courses would need to gain in popularity before being considered for teaching at a university.
A zen student walks up to a hot dog vendor and says, "Make me one with everything."