How to upgrade macOS minor update without updating Safari? I want to upgrade to  macOS 10.14.6 from 10.14.5 but keep Safari 12.1.1 intact instead of Safari 13, which I guess comes with it.

Is there a way to upgrade macOS, but not Safari?

macOS Mojave (obviously), MacBook Air 2017. 



Clicking the top "More Info..." takes me to macOS Catalina webpage.

Clicking the second "More Info" opens the tray below.
I am already on 10.14.6 so can't confirm this but have downloaded 10.14.6 Update (I didn't check the Combo Update) and looking the .pkg with Suspicious Package shows it includes Safari version 12 not version 13.  Note it is 12.1.2 not 12.1.1 as you now have.  



Mojave 10.14.6 Supplemental Update also contains Safari 12.1.2.



It isn't clear why you aren't offered Safari 13 through Software Update.  The Safari 13 Release Notes say 10.14.5: 


  Safari 13 ships with iOS 13 and macOS 10.15. It’s also available for macOS 10.14.5 and 10.13.6.


I seem to remember being offered the Safari update at the same time as 10.14.6 but it may have been a supplemental update or perhaps it changed.  

In any case it appears Safari 13 isn't in the updater packages so you should be safe updating that way.

The Safari Package appears later.