There are three ways I could look at this:
A) Respect. Unless you are making money from your antisocial media, there is no reason why you would keep in touch with other girls there except to line up options like your girlfriend is saying. It's not just about trust, it's about respect. How would it make you feel if she told you every other day about the new guys she is keeping in touch with on antisocial media? It's disrespectful to the relationship. Personally, this is the option that rhymes with me. If the genders were reversed and you had instead come here complaining about her doing what you're doing, guys here would be all over it telling you not to tolerate it.
B) Cynicism. You might say she is concerned because she is going behind your back but doesn't want to lose control over you, and is projecting her own behavior on to you. Personally, I would not go with this option unless I had good reason or a gut feeling to tell me so, because I don't want to live in paranoia.
C) Pragmatism. You might say, if the relationship ends it'll be harder for you to find new prospects than for her since you're a man and she's a woman, so it's more important for you to line up options. Personally I think this makes sense, but is disrespectful.