I have been. I have to admit, it took a while, though. I've said some pretty sexist stuff in the past, and racist, and so on. I don't know if that's the best way to change minds though, but enough people telling me, "Hey, [that thing you said] is kind of sexist" changed my mind.
I would hypothesize that many people are likely to reexamine their beliefs when regularly surrounded (IRL) by people who disagree. We're social animals; we seek harmony with our neighbors, to an extent.
I think Daryl Davis' achievement is changing the opinions of people who are surrounded by supporters. That's much trickier, and killing-with-kindness seems like the likeliest approach there.
i'm curious - was that always the extent of the conversation, or was there ever a 'it's sexist because ... ' part that engaged your reason and changed your mind?
To be honest, the backfire effect played a dominant role and I don't think I was persuaded by that particular instance or any that followed. It was that things I said were called out as sexist many times, and years later I started to realize that I shouldn't be offended when that term is used, and I should be more receptive to people who feel the need to use it.