Gmail have their rules, Outlook.com have other rules.
That's why we have standards ... in this case, RFC 5322. GMail is, for its own reasons, creating a more-restrictive policy than necessary.
That's not unlike Google to do, as they've decided they're the 200 pound gorilla of the Internet and they can create their own standards on the chance that they will, indeed, become standards.
I'm not so sure about this particular one though ...
I have decided to not remove periods in the sign up checking.
Even if this opens up for duplicate account sign up with same Gmail.
You could, of course, have a conditional that checks the domain portion of the address ... if it matches "gmail.com" you could do your checking, otherwise, leave it alone.