Is it necessary to use IdentityUser in asp.net core or asp.net mvc?

If you are using your own code then that is also okay. You can create principalidentity user verifying from your own code so that it will be easy to get current login user in any function or methods. Identity is biuld in, recommended and easy to use in .net solutions.

It is ofcourse not required , but they are provided by microsoft so, no doubt makes life easier, not only this you can easily integrate identity tables with your database and customize them as per your requirement.

if you face any issue on customization then do let us know.