On the matter of women pastors, I've studied the matter twice with an open mind. The first time, in 1979, I did so fully expecting to find biblical support for the practice, and came away disappointed that I couldn't find any. When I again tackled the topic in 2000, I doubted that I'd reach different conclusions, but I was willing to be proven wrong.
This time, I approach it with settled conviction, much as I'd approach a study of the evidence for Christ's literal resurrection. I've reached conclusions about both issues, but study further in order to offer intelligent answers to those who refute my beliefs on both topics...as well as other topics.
Having a firm conviction may, indeed appear closed-minded, particularly to those who disagree with me, but such people may not understand that I took decades to reach my position. Being theologically conservative doesn't mean I've checked my brains at the door. In fact, it may actually mean that, rather than passively accepting the way churches adapt to current culture, I'm willing to conform my thoughts to God's Word. And if so doing makes me closed-minded, well, okay!