Websites are the problem. You can't say "no thanks" to a required form field. (The obvious retort of "well don't shop there" is a no-go.)
I've given "none-of-your-business" data to companies that don't need it for a long time, (e.g. my middle name, shockingly, is your domain name, so weird!) but it CAN bite you if you forget your password and they ask for your birthday as proof of who you are.
I get asked my birthday so seldomly that I always forget what my new forever birthday is going to be by the next time I need it.