My HTC Desire HD crashes when picking up a call. Any ideas how to resolve the problem?

This is extremely annoying. After the last update to Android 2.3.5, whenever I get a call from certain contacts, picking up crashes the whole phone application and resets the SIM. Rejecting the call is even worse, as the ringtone continues indefinitely and the phone blocks all input. There is a support thread about this with other people having the same problem. The solution for re-syncing all Facebook contacts didn't work for me. Has anyone here had the same problem and knows how to fix it?