To anyone needing help with this, I figured out the answer to my own question from this person's post copied below:
blueOrbit
I was having a similar problem, but it went a little deeper. My wife could not receive calendar invites at her Gmail address because her Gmail address is also her iCloud login. My Gmail address is (was) also my iCloud login. I have it working now with a fairly simple workaround. Here are the steps I took:
-I changed my iCloud login to a different e-mail address (outlook.com) and that didn't solve it.
-I created an entirely new iCloud login, but she still could not receive invites
-I tried sending invites to other e-mail services, like Yahoo, and those worked fine
-I tried sending to her throwaway Gmail address and that worked fine
OK, so at this point it definitely appears to be related to the fact that her Gmail address was also her iCloud login. The way I saw it, there were three solutions. Either she had to change her iCloud login, or use a different e-mail for calendaring, or I had to stop using iCloud calendar.
I like iCloud despite its quirks so I didn't want to stop using it. While she might be willing to change her login because she loves me, that's not really practical because there are sure to be other people out there that have the same issue. Asking all of your friends, family, and colleagues to change their iCloud logins because you can't send them calendar invites is kind of crazy. Then I remembered that Gmail allows modifiers for e-mail addresses. You can put periods ( . ) anywhere in the address and/or a plus symbol ( + ) at the end plus a combination of characters.
-So if her e-mail was janedoe@gmail.com, and that was also her iCloud login, then I can send the calendar invite to jane.doe@gmail.com or janedoe+calendar@gmail.comor jane.d.o.e@gmail.com and she'll get the invite.
The trick there is that those other e-mails addresses are not, as far as Apple is concerned, her iCloud login, but they are, as far as Google is concerned, her e-mail address.
