Hm. You’re right, but I’m sure, I got an exception - maybe it was in another version of ezvcard.
The vcard that is produced contains an empty BDAY.
I'm not sure, if an empty BDAY is allowed in rfc.
Also the given birthday will be lost completely when using VCard 3.0.
I understand that this feature would be nice to have. However, it’s not the core functionality of DAVdroid and should (and could) be done by another app, so I’m closing thix.
PS: Maybe there are already such apps available