In case others run into this problem - I could not find a solution on the web:
I migrated from an older Crowd version (2.7.2) using JDK 1.7.x (that matters - also for older versions) ) to the actual version (3.1.2) with JDK 1.8.x (that matters) and ran into the symptoms described under Importing Crowd XML Backup Fails due to Different Locale.
ERROR [atlassian.crowd.migration.DirectoryMapper] Failed to parse date: Wed May 14 18:03:35 +0200 2008
java.text.ParseException: Unparseable date: "Wed May 14 18:03:35 +0200 2008"
at java.text.DateFormat.parse(DateFormat.java:335)
at com.atlassian.crowd.migration.GenericMapper.getDateFromFormattedString(GenericMapper.java:99)
The problem in this constellation is that java changed it's german date interpretion of the month march, which was "Mrz" until JDK 1.7.x and is "Mär" ( the german umlaut for ae in the middle ) from JDK 1.8.x on.
So what you have to do is to find "Mrz" and replace it with "Mär" in the Crowd xml export.
Cheers,
Christian