Since 16 Jun 2017, Apple enforces app-specific passwords:
https://www.intego.com/mac-security-blog/apples-new-icloud-security-requirements-what-to-expect/
This is why access with the account password doesn’t work anymore. This also applies to other apps like Thunderbird etc.
To generate an app-specific password, follow these instructions:
https://support.apple.com/en-us/HT204397
You can then set the account-specific password either in the DAVdroid account settings, or you can delete the DAVdroid account and create it again with the account-specific password.
We have also updated our instructions:
https://davdroid.bitfire.at/configuration/icloudPlease let us know if it works for you!