Not really?
I mean, this is probably a subset of "I don't have anything to hide, so why do I care about privacy?" But I just went to California on vacation, and, sure, I'll tell the CIA all about it if they want to know.
And I'm one of the people who understands why privacy is important. (Or maybe, based on my previous paragraph, you'll conclude that I'm not, I just think I am.)
I don't know. It just... doesn't feel that intrusive, for some reason. Maybe because for international travel, I already have to use my passport, so they already know. (Yes, maybe it's a different "they"...) Maybe because there's already a "do not fly" list, so somebody's hitting that database every time I try to book a flight, and it wouldn't be that hard for them to log the queries against it. I don't know. But as I said, at least to me, this one doesn't feel that intrusive... and I can't really rationally explain why.
Maybe it's arrogance to assume that most people are no more paranoid than I am. But I think that means that most people probably aren't going to avoid booking.com because of this.