Tyler Cowen, responding to a question about whether deeply religious people tend to be generally dogmatic, says this:
I don't know of any systematic evidence, but often I favor portfolio models of dogmatism....That is, most people have an internal psychological need to fulfill a "quota of dogmatism." If you're very dogmatic in one area, you may be less dogmatic in others. I've also met people — I won't name names — who are extremely dogmatic on ethical issues but quite open-minded on empirics. The ethical dogmatism frees them up to follow the evidence on the empirics, as they don't feel their overall beliefs are threatened by the empirical results.
I am, of course, just guessing here, but this doesn't feel right to me. If I had to extrapolate from my experience, I'd say that rigidity of thought is a general personality characteristic, and that people tend to be either rigid or open across the board. Religious fundamentalists, for example, often seem to be political fundamentalists, moral fundamentalists, and lifestyle fundamentalists as well. Curious people tend to be curious about lots of different things.
But there's one aspect of this where Tyler seems right: I often run into people who are generally rigid but have one particular area, usually a specialty, where they understand the level of complexity involved and therefore tend to be more open to alternatives. Likewise, I've run into people who are generally open but have one particular obsession where they're absolutely unmovable. Unfortunately, although Tyler agrees about this, I suspect his advice — "If you wish to be a more open-minded thinker, adhere to some extreme and perhaps unreasonable fandoms, the more firmly believed the better and the more obscure the area the better" — gets the causality backwards. Open-minded people may sometimes develop obsessions, but I doubt that obsessions help you stay open minded about the rest of your life. (Though if the obsession is strong enough, it might make you apathetic about the rest of your life. This is not quite the same thing, though.)