The same thing can still apply. You and I disagree about women preaching. We are both standing on the word of God. It doesn't make sense to keep trying to prove my point, if we don't agree. Leave it alone.
It says in the bible that one plants, one waters, and God increases. No one is ever going to give someone all the tools they need to change.
The muslim and KKK example was just that an example. What exactly are you talking about? I have plenty more. It doesn't have to be as extreme as that. FOR EXAMPLE: my mother has her opinion on what I'm doing in life and got quite heated with me the other day b/c of some assumptions that she made. Now I could have tried to prove that she is wrong, but she would not have heard me. Her mind was already made up. So I left it alone. She would have had an answer for everything I said. I know I'm doing what God has me to do, so I'm not going to argue with ANYONE about my decision. In the end, he will justify me. There was no use for me to get upset with her. Another Example, which is like the situation you spoke of, is this: I was at a dinner party and person A was complaining to me, and person BCD, about how rude, pious, and condescending doctors are to her in her field. She did not know person B was a doctor. Person B had every oppurtunity to stand up and say, we are all not like that. Why didn't she? Who knows, maybe she felt the girls experiences were indeed valid, maybe she didn't feel like it was the time to approach her. Maybe she didn't feel the need to prove herself b/c in the end, her work will stand on its own. Maybe she did not feel like the atmosphere was open for that.
Some people are not going to be open to hear you b/c they either 1. don't know they don't know, 2. your attitude, even though you can be as sweet as pie, 3. they are self righteous can't admit they are wrong 4. they know they are wrong and don't want to listen.
Whatever the reason you don't always have to prove your point, or give your opinion unless the Holy Spirit is leading you.