If it's a game with both genders and the one you choose actually affects the way the story progresses, then I see no weirdness in doing playing as a female character. If you ONLY play as a female character in EVERY game you buy, and never even go near the male option, then I might question that a little bit, but hell, it's still understandable.
If it's a game where the gender has no effect whatsoever on the progression of the story, nor does it even offer any type of gender specific cut-scenes or skits (quite often in MMORPGs) and you only seem to play as the female, then.. Well, I don't know if I like that. Not really my place to judge, but I personally find that to be a bit odd.
Some of my friends do that, and I don't really like it, but hell, it's their choice. When you mentioned that some like to get completely into the role that they are playing... In a regular game that is not an MMO, I guess it won't bother me too much. But in an MMO, that kind of bothers me. To me, it can come off as deceptive. If they are open about their gender, then I don't really have much of a problem with it. If they are asked of their actual gender, and they respond with their role-play gender which is the opposite of their real gender, then they are lying to you and being deceptive and I don't really like that and I don't really like being lied to by random strangers on the internet.
Considering how much society promotes you steer clear of people who pretend because they are probably a 50 year old pedophile man when they say that they are a 17 year old girl, falsifying your age or gender on the internet is bound to get you labeled (sometimes unfairly) as a creepy old fat pedophile. But really, it's not my place to say if some people get their jollies (or just get off) playing as the opposite gender in games. If they wanna do it, then fine. If they lie to me I don't like that, but whatever.