Apple mail and Gmail warning be careful with this message

Some of my email recipients get a warning when I send email from gmail through Apple mail:

"Be careful with this message. Gmail could not verify that it actually came from firstname.lastname@gmail.com..." Two options are given -report spam or report phishing.

My gmail has worked flawlessly for years and this is a recent problem that was reported to me after I installed Mojave.

I reconfigured my IMAP outbox on my iMac. I somehow managed to get to the google page which allowed me to "accept unsafe applications" - apparently Google deems Apple mail unsafe. I accepted. The result was that the message still appears especially for recipients through a wordpress mailing list (but also direct emails to them). The reconfiguration now screwed up the Apple mail on my phone, meaning it doesn't sync with my computer anymore.

The google instructions are not very clear and ask to search for "email client's help centre" for further advice. I could not find any in Apple support either. Please can anyone help?