With the arrival at Driftwood I begann getting suspicious, since a dog on the cemetery only barked at me instead of talking... but I didn't pay attention to this.
When I headed to drift wood on the other hand and ran into all those chicken, that only said stuff like "bok bok", I began wondering.

Apparently at this point, the perk got broken. I read in a forum, that you have to remove the pet pal perk at the Mirror on the lady vengeance and regain the perk in the character screen afterwards.

Edit: it worked for me like described above...

I even only "clicked" on it once with not knowing what it's for. When I realized, it's for respec, I canceled the whole thing... apparently that was enough to kill my pet pal perk xD