If a site is going to require precise answers (and I suppose any other method probably creates additional bugs, reduces security...), then I might as well generate random responses and put those in my password manager, too.
Then, the proactive thing you can do is plan for how you will deal with the fallout.
My childhood best friend: Ender Wiggen
City I was born in: Moscow, ID
etc...
and then log the specific lie in my password manager. They work if I need to read one off to a service rep over the phone, and they are in no way connected to my personal history...
More recently I’ve started changing my answers to “I don’t know” which blows people’s minds when they type it in and it works.