When individuals decide to accept new ideas and viewpoints, this creates conflict with the label they've chosen to apply to themselves. Enough new ideas, and they simply start call themselves something else. A conservative open to too many new ideas will stop calling themselves conservative, and a liberal open to too many new ideas will stop calling themselves liberal. This happens all the time, in both directions - it's the people that change, not the labels.
As another anecdote, I have met many conservatives who are willing to discuss and debate ideas. None of these conservatives I have met has acted or said anything that suggests they believe women are incapable of management.
I have met chauvinists and I have met conservatives. I don't see a whole lot of correlation.
I don't want to turn this into a political debate, but the conservative ideology does lack legitimacy for the most part. The reason the term "conservative" is used is because the person is resistant to alternative points of view as well as information that contradicts their perspective. This is why those who reject climate change are conservatives: they are rejecting or ignoring scientific evidence because it doesn't fit their worldview.
I don't treat conservatives as children. That does children a huge disservice. Children by their nature are curious and they want to learn new things. Conservatives in contrast are stuck in certain mindsets (that revolve around Just-World Fallacy) and are scared of change in general.