TL;DR Don't hide the calendar but customize your circles.
There is so much to dislike about G+ but the one real annoying factor is that it added the birthdays of everyone in my circles. Searching led me to some simple solutions of either deleting, hiding, or unsubscribing to your birthday calendar (WTF). I use the calendar, and the birthday one for actual contacts bithdays so this wasn't an option
After some more digging what you need to do is to remove Google+ specific entries is: