Same as https://forums.bitfire.at/topic/2136/lists-syncing-contents-not? Can you provide logs? Without verbose information, we’re not able to say “why”.
If I understand the situation correctly, the android calender storage supports individual colors for events but no categories, and calDAV supports categories but no individual colors. So neither individual colors for event or categories can be currently used to distinguish/categories different kind of events.
Using a different calenders for each category would be one option to solve this, but I am limited in the amount of calenders I can create.
I think an event color to calDAV categories mapping inside DavDroid would be a nice workaround, that should at least partly solve this.
As far as I know, the android calendar storage only supports colours for whole calendars, not for individual events. A better solution might be to translate categories to extended properties, which the android calendar storage does support. Something like an extended property with name CATEGORIES and content a comma-separated list of categories could be synchronised both ways.
CATEGORIEScould indeed be stored as an extended property, like DAVdroid stores unknown/unused VCard properties as an extended property. However, the ical4j library is not that convenient and I didn’t find out a way to get all properties which are not processed, so that they could all together be stored as an extended property.