Summary:
Problem: Minecraft crashes after logging in to Xbox Live when Windows 10 Game Mode is on.
Solution: Turn off Game Mode from the Windows 10 game bar.

These steps worked for me.

1. Find the Windows 10 Xbox app. Right-click => More => App Settings.
2. Click Reset.
3. Open Minecraft - DO NOT log in to Xbox Live.
4. Press Win-G to start the Windows Game Bar.
5. Turn Game Mode OFF.
6. Back in Minecraft, log in to Xbox Live.
7. (Give the hamsters a moment to start running.)
8. Minecraft starts running smoothly like it used to.
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Details:
About a month ago the Windows 10 edition started crashing on all three of my PCs. Usually on the initial menu, but sometimes in the game very shortly after starting. Resetting did not help. Reinstalling did not either. This one has had me stumped for a while.

I noticed that things seemed to start stuttering right after Minecraft would log in to Xbox Live. So, I went in to the app settings for the Windows Xbox app (the app is just called Xbox) and reset it. Doing this keeps Minecraft from automatically logging in to Xbox Live on startup.

Without logging back in to Xbox Live, I would then run Minecraft and NOT choose to log in to Xbox Live. Running as Steve, everything worked great. As soon as I would log in to Xbox Live, Minecraft would start stuttering and would soon crash.

After trying all sorts of other things, I finally remembered that Windows 10 has a game bar that you can invoke by pressing Win-G. This game bar gives you the option of running games in Game Mode. Game Mode is supposed to improve the performance of games running on Windows 10. I thought that maybe running in Game Mode might help since I do have an older PC. While running Minecraft, not logged in to Xbox Live, running as Steve, I pressed Win-G. It turns out that Game Mode was already turned on (though I don't remember ever doing that). I clicked the icon to turn Game Mode off.

After turning off Game Mode, back in Minecraft I was able to log in to Xbox Live. At first it seemed like it was going to freeze again, but after a very brief pause, everything starting running normally like it always did. I repeated this process on my other two PCs with the same positive results.