Yes, if you want to know if two addresses refer to the same account, you need to keep up with the actual rules for each provider that you decide to care about.

But, if you're using the email as a username just for convenience, you get to decide what rules you have for username comparison. You can absolutely decide that A@gmail.com and a@gmail.com are different accounts for your service, even though emails you send to these accounts will likely reach the same inbox. You can also decide that they are the same account, but that haşim@gmail.com, HAŞIM@gmail.com and HAŞİM@gmail.com are all different accounts. It's entirely up to you to know what is important for your users.