Anthony has responded critically to the idea that one must be a believer in order to understand theology, and a related criticism follows in the comments on the relationship between belief/orthodoxy and the vocation of the theologian. I'm inclined to agree with Anthony and Adam here... on a bare empirical level, lots of theology seems to get done and understood by non-believers. More substantively, the contributions of theology to the understanding of the faith do not seem obviously to require a right relationship with God. Why would they, exactly? And what concern is it of ours if a theologian is not of the fold? Christ says of the exorcist who is not a disciple that whoever is not against Him is for Him. If the theologian isn't charged with casting out demons, on what basis would we hold them to a higher standard than those who did such things in the scriptures?
Adam also makes a good point in the comments about theology as a critical reflection requiring distance from belief... what we do as theologians puts the possibility of childlike faith in serious jeopardy, and we would do well to take great care in recognizing the risks of our critical work if it is to remain edifying for the churches. We do not (I say this as a believing theologian, at least) pursue critical inquiry in order to criticize the faith. We use criticism to engage with theories about the faith (those made explicit as well as those left without explication), in order to gain better understanding.*
With regard to our own souls, I think that the theologian is something like the rich man trying to get to heaven; a great amount of knowledge carries with it an increased difficulty in recognizing that "where there is knowledge, it will pass away." Anyone who pursues a path of theology should regularly pray for the safety of their own soul, because while the work of theology is often joyful and inspires faith, it can also do quite the opposite. Theology is not in itself a pious profession... at base it is a theorizing task, and it only serves piety when piety uses theology as a tool for understanding.
I would also add that while I don't think one needs to be a believer to be a theologian, and further that theology is even tied in important ways to the possibility of unbelief, I do think it's fair enough to say that the believing theologian should at least be the normative model for theological work and that unbelieving theologians will probably always be an exception to the norm. This is not merely a statement of institutional exclusivity or a prioritizing of orthodoxy. Theological work requires an entertainment of the truth of the faith in a more basic sense than it requires a suspension of belief for the purposes of critically reflecting upon the coherence of beliefs. What distinguishes constructive theological work from other critical engagements with religion is its assessment of the value and meaning of the faith itself. A preliminary recognition of coherence seems to be required in order to meaningfully do something with the faith, and so it seems understandable that believers look on unbelieving theologians with some wariness... not even because they will corrupt orthodoxy (believing theologians do that well enough on their own!), but simply because there are no strong reasons for constructive aims concerning a faith that does not carry any meaning or value. And while the meaning or value of the faith may be identified elsewhere than the truth of its teaching (a non-believing theologian may legitimately find the faith valuable for philosophical, ethical, societal, political, etc. reasons apart from the theological truth of its Gospel... as Adam says, you just need to "care" about it), the Church's teaching does recognize a space of orthodoxy as its own norm, and adherence to this norm in life and thought is the most obvious basis upon which one would do theoretical work with Christian teaching. To say this is a far cry from saying that theological knowledge is a divine gift predicated upon a reception in faith that excludes non-believers from practicing or understanding theology, but I do want to recognize that theologians working from a dogmatic framework with an assumption of faith have good reason for doing so, and that non-believing theologians working within the Christian tradition should expect various traditions of orthodox and heterodox Christian teachings to set the tone for what is recognized as typical theological work.
*Here I'd want to offer some qualification to Adam's comment about arguing for the truth of the faith requiring critical distance. I agree with what he says, but it should also be said that not all theology argues for the truth or falsity of any tenets of faith. If theology is being done simply to better understand the meaning of a confession of faith, or to entertain various speculative options, or to mediate differing understandings, tasks like this don't seem to require being "open to the possibility that [the Christian tradition is] not right" if by this he means raising the possibility of an abandonment of a broad adherence to the faith. Such openness to abandoning belief seems to only be a necessity for apologetic tasks in theology, where one presumes to stand as judge over the truth of certain assertions.