My relationships are very important to me, and my people are a large part of my life. If I started seeing someone who didn't want to know anything about them, even the regular day to day stuff (not the intimate parts), that would be a big red flag for me.
On the other side of the coin, when I'm seeing someone new, I really want to know about his or her other relationships. First, if I'm into someone, I want to know everything about them. Second, as a new person, it's very important to me to be respectful of those relationships.