Is it foolish to give out your real name and email on a site like Yahoo Answers?

I wouldn't, you can't trust anyone nowadays, everyone is always pretending to be someone else. 

Yes, all social media is linked with a communist regime that wants to make merchandise out of you.

I think it could be dangerous, but it's more likely to be embarrassing. You really can't be sure who is on the other end of the email. Yahoo allows members to safely email other users without giving out personal addresses. It's a much safer option.

It's not so bad if you are fine upstanding citizen like myself, but if you were a dodgy debt collector there certainly could be repercussions. 

Probably not dangerous, but ill-advised if you don't already know the person.