The latest news on last week’s macOS updates is that the Mojave update to 10.14.6 does appear ‘safe’, and Apple has now made the two security updates 2019-004 to Sierra and High Sierra available again, apparently with previous bugs fixed.
The problems appeared to be in the BridgeOS update, which is specific to Macs with T1 or T2 chips. The version of BridgeOS or iBridge, 16.16.6568.0.0, which first shipped with these updates appears to work correctly in the 10.14.6 update, but could cause problems with sleep and wake in the Sierra and High Sierra Security Updates 2019-004.
At its worst, this resulted in the updated Mac suffering a kernel panic either when it tries to sleep, or when waking from sleep. Disabling system sleep is a workaround for the time being, which probably isn’t too disruptive for desktop Macs. However, most users of MacBook Pro and MacBook Air models expect their computer to sleep when they close its lid, and to wake on opening. If either of those actions cause the Mac to reboot because of the kernel panic, this is extremely disruptive. The same basic workaround can be used, to shut the Mac down every time rather than let it sleep.
If you have already applied this update and are suffering from these or similar problems, one potential solution is to upgrade to Mojave. Some users have reported that this is a reliable fix, if you are ready to upgrade.
As explained here, these or the App Store updates should now be safe to install at last.
I have so far been unable to locate any information from Apple, but am particularly grateful to Al Varnell and Mr. Macintosh for their help and information.
Last updated at 2105 UTC 29 July 2019.