Latest macOS Mojave update (10.14.4) and Mail.app Google accounts issue
No.

The update broke access to some Library configs that are under control of System Integrity Protection(SIP).

Boot to the recover console, disable SIP with 'csrutil disable' in the terminal, then boot into the OS, go into Internet Accounts and select Google as normal.

After following the steps to give your Mac permissions to your Google objects(mail, calendar, etc.), boot back into the recovery console and re-enable SIP by running 'csrutil enable'. Boot back into the OS and compute on.

I got the hint to do this by looking into the console logs in the console utility, but I have no idea which log I searched for 'google' or 'accounts' in, but I found a problem mentions an error with a 'file-write-xattr', so that gave me the idea that SIP was involved.

Someone should be able to track down the issue and get the errant permissions logged with Apple so the fix can go out with the next patch, or set a sticky here with a more detailed explanation and fix, and not just a work-around.