Seems to happen when switching different fonts, but not within the same font family, if that makes sense. Going from SegoeUI to Liberation Sans showed the behavior, but changing font size did not for example.
On the Now Playing tab (Playing Tracks view)
"Keep Columns Sized to Panel" and "Auto Size All Columns" both off
Edit->Edit Preferences->Layout(1). Change default font.
Hit "Restart"
When MusicBee restarts, you are not able to resize the columns until either:
1. Switching "Keep Columns Sized to Panel" on and off again
or
2. Switching to a different tab and then back again
Also, the majority of times I tried, "Restart" results in the misalignment of the columns until you switch to a different tab and back again. Can't say it was every time like the column resizing for sure, though.
This is in the MusicBee3 skin, if that matters.
EDIT: I just closed and reopened MB without changing anything during the previous session. Opened to the "Now Playing" tab, and the columns are misaligned and I'm unable to resize them. Doesn't seem to be related to changing the font now. Don't know what's happening.
Here's what it looks like when I open it:

And here's what it looks like when I switch to the Music tab and then back:

Note the data in the colums are in exactly the same place in both, but the column headers are shifted.