I updated to 10.14.4 and both of my Gmail accounts will not function in Apple Mail. It keeps asking you to sign in, but then still won’t recognize the accounts. Out of frustration, I gave Airmail another try and I must say it is a much-improved product. Maybe I will actually stay away from Apple Mail this time.
I upgraded to latest Mojave, Gmail is working fine.
Count yourself lucky, seems to be thousands with this issue
If this link is accurate, it’s only an issue with G Suite accounts. Regular Gmail is fine after one sign-in. http://www.iphonehacks.com/2019/03/gsuite-users-reporting-sign-in-issues-mail-mojave.html
As a happy Mailplane user, I didn’t notice. 
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It killed both my G Suite and personal accounts.
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I went ahead and upgraded after reading this topic to see what woudl happen. 
I figured I could fall back on Spark or Airmail temporarily if needed. However, Mail app is working fine for my G Suite and personal gmail accounts.
I upgraded to 10.14.4 a few days ago. There was one request to sign in to Gmail; works well now. I’m using Apple Mail to access my Gmail accounts. These are personal, not business accounts.
FWIW. I have a Googleapps mail account through my university and a personal Gmail account, all in my Apple Mail (along with 5 other non-Google accounts), and haven’t seen a problem. Hope that keeps up!
It seems to have caused it to not always be connected. The first day I had to sign in at different times to my 2 gmail accounts that I have on Apple Mail. Once that was done I haven’t been asked to log in again but I’ve noticed the not connected symbol appearing more frequently next to those accounts than ever before.