This seems to be the same problem as https://forums.bitfire.at/topic/1100/v1-0-9-http-1-1-415-unsupported-media-type
Please use DAVdroid 0.9.0.1.
Every time I change a contact I get a sync error.
It seems that DavDroid is not creating a valid VCard anymore (all the contacts were synced with an old version without a problem)
I attached links to three examples, as Im using the service of my mail provider I cant say if its related to a change on the server side, other tools like SoGo Connector are still working so.
(Actually I cant see a misstake in the Vcards sent by DavDroid but I am also not skilled in reading them…)