How to get calendar invites to come in as iCal and not as Google Calendar invites?
Or do I have to use a non-Google address as my Apple ID?


No, you need not change or create a new Apple ID. A calendar invite sent to an email address registered with Gmail will automatically get added to Google Calendar. Also, it won't automatically get added in Apple Calendar.

You can do subscribe to your Google Calendar in macOS Calendar app. The instructions to subscribe can be found in the following links:


https://support.google.com/calendar/answer/37648
https://support.apple.com/kb/HT202361


However, it is not possible to get the calendar invite via Apple ID in iCloud calendar.