My wife plays a mean Krogan.
Buy what does she play on ME3? boom boom
Playing a different gender character makes no difference - all it does is adding to the variety. (And a chance to look at a female bottom a whole match.)
Playing with a different gender player makes no difference either - all it does is adding to the variety. (And a chance to listen to a pleasant voice.)
I know several posters in past commented that the female nova guard makes a less annoying/more pleasing grunt noise.
I have been mistaken for a girl when playing asari. That is more bizarre in my opinion.
This happened to me years back when I was messaged asking if I was a girl or not (whilst playing an asari). I'm assume it's just players who don't know anything ME lore.
It wouldn't be surprising if some people showed a preference for kits of the same gender as themselves, but most people don't, and what that person said to you is literally one of the stupidest things I've ever heard- that girls should only play asaris and furies? Really? 
I have a preference for playing the same gender in single player. In multiple player it's all about the abilities and good on Bioware for having female characters with good and different range of abilities so you want to play those characters.
Play whatever YOU are happiest with.
This game is meant to be for fun and you shouldn't be railroaded into not doing something just because of your gender.