NOT?!
You probably have a couple of sites, usually banking or investment, that require you to answer several 'personal' questions. Things like where you were born, favorite teacher, best friend, first pet's name, etc. (Too) Many sites use exactly the same, generic questions. That means when (not if) they get hacked, your info may be compromised at other sites. Just like using the same password is silly (or worse!), using the same answers to the same question is not very smart (or worse)!
But, you say, "I have a hard enough time remembering my first pet's name without trying to remember one's I make up!" Agreed, but that's the big advantage of a password manager.
A good password manager will allow you to generate random text entries for any field you need to fill in at a site. Hopefully, you're already using these types of generated passwords, if not, welcome to the 21st Century!
But why put actual, usable, personal information anywhere you don't have to?
Since you're using a good password manager, you can put any text the site will accept as an answer and never worry about remembering it, that's why you have the password manager.
It may be time we stop calling these apps "password" managers! A good one will do a whole lot more than manage passwords!
Of course, you probably need to be truthful when communicating with the IRS and other government entities.
OTOH, you don't have to worry about the NSA, they already have all your personal info!