My understanding is that MUI4 for 68K is somewhat unpolished/unstable. I wonder if you'd have better luck with MUI5 which has been refined a bit further? There are almost no user-level differences between 4 and 5, although I don't know what's changed internally.
But before you try that, I remember years ago when MorphOS moved from MUI3.9 to 4.0. There are significant differences in how 4.0 handles prefs settings, and loading in a prefs file from 3.9 was leading to all sorts of bizarre rendering and layout errors. So it's possible MUI4 is choking on your IBrowse MUI3 settings so badly that it's causing a crash.
To verify, delete or temporarily rename ENVARC:mui (I think that's the path...don't have my Amiga in front of me to check) and reboot, which should reset all your MUI settings. Hopefully the defaults will get your programs back to normal, but you'll have to go through and manually set all your MUI preferences again.