While I'm not a girl, I did identify with Max quite a bit; very introverted, a bit of a shutterbug (nowhere near the level that she is in terms of dedication or skill, but I do like messing around with a camera), tendencies to having smaller circles of friends. Even had a good friend from childhood that I lost touch with when they moved (never really got back in touch again and I'm not aware of hard feelings, but it was something I was thinking about during the scenes where Max and Chloe are rebuilding their relationship). Also very much appreciated the (possible) representation when the principle's office scene showed that she she was in a special ed. program for people with learning disorders.
@Mostro789 I always took Max to be bisexual, too, given that there are non-choice-based comments about her being attracted to boys (her early journal comments include thoughts about finding a boyfriend, having a mild crush on Mark Jefferson, the observation that she's attracted to skater boys in episode one, player choices that can angle her into reciprocating Warren's feelings for her, etc.) and her falling in love with (or at least questioning if she's in love with) Chloe is pretty well documented.
On the other hand, I could see a case being made that Max was lesbian and references to her liking boys were assumptions she made before she started to figure herself out. (I know that's what I took Chloe's story to be, given that the games referenced her having boyfriends in the past, but her expressing disgust at the thought of dating a guy in the present, but I've seen cases made that she was actually bisexual, even if she had a stronger attraction women.) I guess the specifics are somewhat left to player's interpretation, given that none of the character's self-identify what they are.