Ideas for a political philosophy/theology dissertation

I can’t help you with how prescriptive the dissertation can be (that’s something only your university department will know), but there’s an extensive literature in political philosophy on the relationship between religion and politics. Much of it focuses on what the role of religion ought to be in the liberal (particularly Rawlsian) state, and whether that role is adequate. More specifically: Rawls argued that the liberal state ought to be neutral between different conceptions of the good (of which different religious beliefs are a paradigm case), and that policies and laws should never be defended solely in terms of specific conceptions of the good. The question then is what role does this understanding leave for religion and religiously-based political beliefs in the public sphere?
If that sounds interesting, Liberalism’s Religion by Cécile Laborde looks like it might be a good place to start (though I haven’t read it). You could also search in the index for specific sections on religion in the works of Rawls, as well as his ‘communitarian’ critics such as Sandel, MacIntyre, Taylor, and Walzer.