For some time I have had a dozen or so BibTeX databases with permissions set for both user and group to write to them so that anyone in the group can update the database with new entries. Before 4.10, Kate gave a warning but happily wrote the changes to a database owned by another user. Since I installed 4.10 Kate will no longer write to a database even when write permission is set for the group.

Is there a fix for this or should I report it as a bug?

Does Kate give a error message or anything else which indicates why this may be an issue?
One thing I can think of is that it is trying to create a backup file, which is failing as a operation. You can disable this in the Kate settings.

Another thing it could be is KSaveFile - which attempts to protect data integrity. It works by writing the full contents out to a new file, and then replacing the original file with that new file. If your user does not have write permissions to the directory containing these database files, then this will not work.