[MC-137300] ConcurrentModificationException thrown when upgrading world

The bug

Converted worlds produce the error below in constantly when flying around, and chunks that should get loaded are not being loaded as seen in the screenshot.
The example log took me ~30 seconds to get a few erors.

[16:38:58] [Server thread/FATAL]: Error executing task
java.util.concurrent.ExecutionException: java.util.ConcurrentModificationException
	at java.util.concurrent.FutureTask.report(Unknown Source) ~[?:1.8.0_181]
	at java.util.concurrent.FutureTask.get(Unknown Source) ~[?:1.8.0_181]
	at k.a(SourceFile:200) [1.13.2-pre1.jar:?]
	at net.minecraft.server.MinecraftServer.b(SourceFile:726) [1.13.2-pre1.jar:?]
	at net.minecraft.server.MinecraftServer.a(SourceFile:681) [1.13.2-pre1.jar:?]
	at dgh.a(SourceFile:131) [1.13.2-pre1.jar:?]
	at net.minecraft.server.MinecraftServer.run(SourceFile:584) [1.13.2-pre1.jar:?]
	at java.lang.Thread.run(Unknown Source) [?:1.8.0_181]
Caused by: java.util.ConcurrentModificationException
	at java.util.HashMap$HashIterator.nextNode(Unknown Source) ~[?:1.8.0_181]
	at java.util.HashMap$EntryIterator.next(Unknown Source) ~[?:1.8.0_181]
	at java.util.HashMap$EntryIterator.next(Unknown Source) ~[?:1.8.0_181]
	at bnj.E(SourceFile:1162) ~[1.13.2-pre1.jar:?]
	at java.util.concurrent.Executors$RunnableAdapter.call(Unknown Source) ~[?:1.8.0_181]
	at java.util.concurrent.FutureTask.run(Unknown Source) ~[?:1.8.0_181]
	at k.a(SourceFile:199) ~[1.13.2-pre1.jar:?]
	... 5 more

Code analysis

Code analysis by [Mod] md_5 can be found in this comment.