I'm not big into social media so I'd prefer a guy who isn't as well. And I couldn't care less if our relationship is not officiated on socmed. I personally would not post any photos of him either.

It depends on the person really and how they are acting on their social media. If she's still actively representing herself as single to get all the attention, then you'll need to have a talk with her to communicate how you don't feel comfortable with her doing that. That's definitely a red flag if he/she is being defensive about it. Communication is key.