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.