Why does TicketOne ask for your birthdate and city of birth when you register to buy tickets?

It sounds like you are booking through a third party. Why not buy your ticket directly from the gallery?

Thanks, we are. The official Borghese Gallery website takes you to tosc.it (TicketOne) to reserve your tickets. In order to proceed, you have to register with TicketOne and it asks for birthdate and city of birth, which seems unusual but I was wondering if in the EU this might be expected?

I was in France two months ago. We bought a lot of tickets on line and we never encountered those questions so it's not an EU thing. It seems very strange.

I bought those tickets last year and don't recall having to enter that information.

Borghese website links to three different vendors to obtain tickets. Looks like the lowest price option is Ticket One. Be sure to look carefully as the sites are designed to lead you to the higher priced tickets. with added tours.
All tickets are timed entry and allow you two hours to visit the museum, which is generally sufficient.
As for the birth date and birth city, could be part of a security scheme, would not worry about it.