There's no way to win this. Include social media signin, the "ZOMG PRIVACY" crowd yells at you. Don't include them, and the "ZOMG EMAIL ADDRESS" crowd yells at you.

Not directed at you specifically, but people waste more time complaining about signin options than actually going through the process. It's kind of funny.

You can do both.

ditto, google/twitter/facebook/github are all ok for me, just don't make me type my email again.

Prefer google auth too myself, but a nice workaround is the text expansion feature in iOS where if you type in the first three letters of your email it auto fills the rest.