Thanks - I wasn't award that I could hide the info (it certainly wasn't made obvious by the dialog). I still think that forcing me to fumble around in G+'s settings to do this is unnecessary (although I can see why Google is doing this!).
I feel similarly. What I've been doing is just deleting my G+ account each time Google creates it, but if it becomes too much of an issue, I will be forced to switch. A real pity - I love gmail.
This would be an ideal solution for this situation, but the problem remains: if I cannot authenticate via the 3rd party initially, the service has no way of knowing that I am actually the owner of the account. I am not sure what the working implementation of this looks like.
If Google just wanted me to add a few relevant details to my primary account for some obvious useful purpose, details that would be kept private, I would happily oblige. However, this goes beyond that: Google is asking me to share information with no apparent application use (birth date?! gender???) to ANYONE who stumbles upon my G+ profile. I am not against unifying their services - in fact, this is what Google's basic authentication service should and could have done - but that is not the full extent of what is happening here, as far as I can tell.
You may well be correct - I only noticed this now as most of the sites I frequent are not linked to my Google account. I know YouTube has been bugging me to put in a Real Name for a while, but I was never prompted before to create a fully fledged G+ profile (incl birth date, gender...)