If you're going to ask me an extremely personal question, just ask it. Do not hedge with "you don't have to answer this if you don't want to." I know I don't. I don't need permission to decide what comes out of my own mouth. Giving me your permission to respond as I see fit is patronizing and more likely to make me go Scandosotan and clam up on you. It's less likely to get your question answered, and it's less likely to get me to volunteer similar information later on.
(Even "I hope you don't mind my asking" is a safer hedge with me, because it indicates that you know you may have crossed a line in asking, not that I may have crossed a line in refusing to answer.)
I'm perfectly capable of saying, "I don't think that's any of your business" or "I prefer not to answer that question" or "I'm not going to talk about that right now" or "My goodness, why on earth would you ask me that?" I'm perfectly capable of carrying on a civilized conversation afterwards. I won't hold it against you if you ask a question I don't want to answer, unless you keep asking or act like I owe you the information. But I don't need your permission to speak or not to speak. EVER. That's not the world we're living in. And acting like you're handing out permission where you have no authority is not a good way to deal with me.