Now the game loads further, but then for some reason I get a "Saving world" screen for a second, and the game crashes again with this:
The game crashed whilst rendering screen
Error: java.lang.NullPointerException: Cannot read field "existingSave" because the return value of "com.epherical.serverbrowser.client.CommonClient.getInstance()" is null
Exit code: -1
Crash report: https://pastebin.com/sQc9V3VW
Also, if it is important, the modpack runs without issues on another PC.