"I want to prevent users from creating multiple accounts"
Maybe, like the others here say, that is not a good reason to ignore periods.
However a good reason can be to prevent users from accidentally creating different accounts. Let's say, a web app has recently been installed, and not yet configured to work with Gmail OpenAuth. So people type their addresses manually, to sign up with local email + password accounts.
Later, the web app configures OpenAuth and a Sign in with Gmail button. Now people with a gmail address, click that button to sign in. And ... in some cases, people accidentally manually typed their addresses with no dots, or with dots, or different dots, when they typed by hand (well, keyboard) previously.
Now, the app thinks the addresses are different, and auto-creates a new account for the user. S/he then wonders: "Where is all my old stuff? That I created before with this account? I logged in with the same email address!"
Real life example of this happening: https://meta.discourse.org/t/discourse-creates-new-users-if-dots-are-present-absent-in-google-email-address-when-logging-in-using-google/66151
I would think that for non-technical people, ignoring dots in Gmail addresses is the user friendly approach.
To let technical people create many accounts using the same Gmail addr (for testing purposes), you can choose to consider whatever+with-tags@gmail
a different address. — Everyone happy :- )
(Astroturfing & spam filters can take into account that [email protected]
and [email protected]
is the same person.)