Can I publish my profile picture for all users of Mac Mail? When you open an email from someone in Mac Mail, their profile picture (set in the Contacts app) is displayed. If a profile pic is not found, a circle with that user's initials is displayed.

Is there a way to publish a profile pic associated with my email address, so any user of Mac Mail can see that profile pic when I send them emails?

For Gmail web clients, I need to set a profile pic in Google+. For the Fastmail web client, I need to set a profile pic on Gravatar. But I don't know of a way for Mac Mail. Is there one?
There is no way to do this.

The Mail app on the desktop only retrieves profile pictures from the local machine, that is, from the Contacts app, from your user account, and from ~/Library/Images/People/.