I just tried your suggestion, but sadly it doesn't help a thing. Whenever a font is installed, let's say a random one from Dafont.com, InDesign crashes. Once I remove the font, the application crashes..
It's so strange. I'm on a completely clean machine.
How about a font from a reputable vendor like Adobe or Linotype? ID has a history of not liking free fonts.
I haven't got any bought fonts (yet). However, for testing purposes I'm not buying one. But that would be strange. I'm using InDesign for over 4 years now without any problems. Now, I updated to CC 2015 and this issue starts to pop-up. Before I cleaned my system, I was on CC 2014.
Three things only changed:
1. I formatted my drive / I wiped all files
2. I updated to a new OS (Yosemite -> El capitan)
3. I updated from CC2014 to CC 2015.
Update: Oh that's strange. As of writing, even without a custom font, InDesign crashes. However, as I wrote, before whenever no custom fonts, it worked. With custom fonts, it crashed. So it should be related..
As a Windows user I can't say a lot about Mac OS and ID, but we've had plenty of reports of troubles with CC 2015 on Yosemite, and they're starting to come in for El Capitan. Can't hurt to trash your prefs. See Replace Your Preferences