iCal invites sent to my Gmail address (which is also my Apple ID) get added to iCloud
If your Apple ID is a Gmail email address, and someone sends you an invitation from an Apple device, your Gmail account won't get the invitation, but it will be added automatically to your iCloud calendar.
Why? Because your Gmail email address is recognized as an Apple ID, and that takes precedence: the invitation is added to your iCloud calendar instead of being delivered per email.
That's the default behavior, but fortunately, it can be changed to behave the way you want, as explained in this thread on Apple Communities:

Log in to https://www.icloud.com with your Apple ID.

Open Calendar:


Select Preferences from the gear icon:


Select the Advanced tab and, under Invitations, check &quot;Receive event invitations as: Email to &lt;your Gmail address&gt;&quot;:


Save the settings.


Now you should receive invites per email instead of being automatically added to your iCloud calendar.