I noticed the Fide rating list is always published with the date of birth of the player. Is registering one's actual birthdate with Fide a requirement for a Fide rating? It is a major concern for me given the rise in cases of identity theft.
Yes it is.
All player's data are obligatory for online registration in FOA. For players registered by the National Rating Officers or the FIDE Rating Administrator, first name, last name, gender, date of birth, e-mail address and Federation are obligatory for a successful registration.
I noticed the Fide rating list is always published with the date of birth of the player
That is not true. The full date of birth is now never published, although in the early noughties it was. Now just the year of birth is published.
Furthermore that is often also not published. When you register you can request that your year of birth is also not published. To verify you can go to the "Advanced Search" on the FIDE rating website and search for female players from various Arab countries. If you do that you will see that for some of the countries many of the women have blank for their year of birth.
Example: United Arab Emirates.
Is registering one's actual birthdate with Fide a requirement for a Fide rating?
FIDE require that to allow them to differentiate between two players with the same name. It does happen occasionally and then date of birth is essential. They don't need to publish even your year of birth. Once registered your FIN is enough to identify you in the system, and you can request even that is not published.
It is a major concern for me given the rise in cases of identity theft.
You are wrong to be concerned. Your full date of birth is never published, only the year, and you can request that not even that is published.