My experience:
After Safari 13.1 + 2020-002 Sec Update (applied at same time). I had reboots during:
Leaving Mac mini 2018 running with Safari Open
Leaving Mac running with Safari Closed
Reboots during sleep
Reboots if set to never sleep.
"Solution": Reinstall 10.14.6 from previously made thumb drive (long before 2020-002 Sec Update published).
Then run this line in Terminal:
sudo /usr/sbin/softwareupdate --ignore "Security Update 2020-002"
Now SW update won't ask me about that update...But, I DID reinstall Safari 13.1 update, because I was at 12.x after the os reinstall, and had a lot going on in safari that I didn't want to lose.
I also did: sudo /usr/sbin/softwareupdate --ignore "macOS Catalina"
super awesome results there! Highly recommended if intending to stay on Mojave... of course now we have this annoyance that is conveniently migrating people away from 32 bit apps and their super productive "legacy" lifestyles that Apple is determined the expunge from this earth...
This same format works for other updates too. To stop ignoring those updates:
sudo /usr/sbin/softwareupdate --reset-ignored
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UPDATE: See this:
https://www.macrumors.com/2020/05/28/macos-ignore-software-updates/
to remove the badge even after updates are ignored, and all this:
With the release of macOS Catalina 10.15.5 and related security updates for macOS Mojave and High Sierra earlier this week, Apple is making it more...
www.macrumors.com
apparently they've deprecated the --ignore flag for major system + OS updates... sigh... so, if you update to Catalina latest service release 10.15.5, OR on Mojave and update to Sec update 2020-003, this will get you...
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I of course did all the normal maintenance stuff, run cocktail, zap pram, reset smc, play nice, etc.
I just rebooted right now, and when I logged in I got the message of KP. Even though reboot process appeared to go okay, but can't be certain it wasn't slower than usual etc... I reinstalled this bug a couple days after I got it and stumbled on this to confirm it was the 2020 sec update. Also saw that people were saying a Firmware update was rolled into this, which can't be rolled back by the end user on these "T2" chipped systems.
I have come back to this thread to see if 2020-003 Update + Safari 13.1.1 updates have solved the problem. We have at least one report here above that says the -003 update didn't fix it.
As of right now, I don't have time to mess with this, so I'm not updating to -003 + Saf 13.1.1
I'd be interested to know of results with a sample size greater than 1 for people who haven't tried rolling back the sec updates yet.
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UPDATE EDIT June 1st: if I manually put my system to sleep, it now reboots instead......... automatic sleep using energy saver preferences doesn't seem to do it again, yet...
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Thank you to those reporting to apple, even if getting sh*t responses.
I would expect no less from Apple at this point.
I too am in the same boat, with still a couple HIGHLY necessary 32 bit programs...
So, cloning our drives before updates can't always solve issues like this! Because the FW gets "secretly" updated too! I didn't see any obvious information that the FW was being updated with -002. Does anyone know where this might be visible so NEXT time we can all think twice about doing such an update until the bleeding edge people have verified it's not gonna screw us over after supporting apple for 30+ years? Insert unkind things here.