This is an old thread but recently I had the same question and could not find easily an answer.
In short, hinoki appears to be bird safe. It is frequently used for hot bath here in Japan as it is quite resistant to mold. I asked my wife to look for info in Japanese as this wood is common here and we found several websites listing it as safe, and apparently experience of people sticking with making toys with hinoki as it is safe. I bought two boards of hinoki to make some plateforms, but still did not do it and I will still search a bit more info and experiences online to confirm it is safe. And of course, once I make the plateform there will be a careful watch at first to make sue there is no bad reactions.