[Galaxy Tab 8.9 General] codertimt:
Well, I do have a working tablet again, but unfortunately don't have an exact procedure documented for a fix. I found a couple different threads online where other platforms are having the same issue and it has been tracked down to the latest play services using NEON instructions that are not supported by the older Tegra platform. And, as it's been over a month now, it's not clear if it will be fixed.

The basics of getting things working are to have file manager with root access available to you without wifi. It's possible that exactly what folders need to be created in /data/app/ depends on your Android version. I am working with the latest 7.1.1 build and all instruction I saw to create a folder named com.google.android.gms-1.apk and com.google.android.gms-2.apk did not work. At least not by themselves...on my successful attempt, I created them still, but also created a folder com.google.android.gms-1 as that is where the update came down on my system...so I deleted the existed folder of that name and created an empty one. Again, I don't have an exact procedure...but I will line out some steps that might help someone...

Have working, rooted 7.1.1 install.

Download opengapps from 20170119, phh superuser apk, root file explorer apk.

Factory reset in recovery, install opengapps, wipe cache again for giggles.

Go through setup without setting up wifi, install phh, install root file explorer.

Create folder /data/app/com.google.android.gms-1...maybe the other 2 mentioned above also.

Enable wifi and continue with life. You will have to sideload older versions of some google apps. The latest Google Maps wouldn't work for me...I just searched for the last version before that magic Jan 19th date...that seems to be working fine.

Caveat to this is that this is not exactly what I did to get things working...it is what I think should work. I was actually trying to follow another post that was trying to use a system app remover app to downgrade the google play services...never could get it to work...but stumbled upon something that did work...so I'll lay out those steps...

Have working, rooted 7.1.1 install that has crashing google play services.

Disable wifi

Create the folders mentioned above in /data/app.

Go to Settings->Apps->Google Play Services->Disable. This allowed me to roll back the install of the latest Google play services.

In my case it rolled back to the very previous version..because that is the version I installed from opengapps in recovery...it might roll back to whatever was originally flashed. In that case you can find a 10.0.84 google play services apk...I could never get it to install on mine...but that might have been because I already had a newer version when I was attempting to install.

Enable wifi and possibly sideload some stuff like above...

So, for other Android versions, steps should be similar...perhaps that's when the folders ending in apk will come into play. If there was a reasonably priced >8.5" and <9.5" tablet...preferably with 16:10 aspect ratio and higher pixel density than the Galaxy Tab 8.9 I would buy it...unfortunately such a device doesn't exist. May look into a used Nexus 9...until then it appears I am at least stable again...