I'd like to mention a few things about supposed gender-specific frames of mind:
If there are such differences, they're statistical trends. Women will be more likely to think X rather than Y, men to think Y rather than X. This will not apply to every single man or woman you might find. Apart from the plain facts of biology, our brains are immensely malleable. Because of this, personality traits are usually - and rightly - regarded as gender-independent, and I wouldn't want to see that changed. In general, I would prefer - no, I do require - dialogue to be gender-independent in order to facilitate roleplaying.
What I do not want - and this is what ME did wrong - is for male stereotypes to intrude on the behaviour of my female protagonists without giving me a choice. The problem of ME wasn't that it didn't consider gender, it was that it was made with a male stereotype in mind. Sometimes this resulted in a nice bit of trope subversion if you played femShep, but in other places it just gave all of my Shepards - male and female alike - traits I didn't want them to have.
I also think it is OK - maybe even desirable if used sparingly - to play with (and possibly subvert) a fictional culture's preconceptions of what is male/female behaviour and make gender-specific dialogue with that in mind. However, the way we walk is not independent from culture. Beyond the basic physical attributes resulting from "walking on two legs with one joint that can bend in only one direction", It's not a fact of biology and shouldn't be treated as such. Thus, the MC's walking/running animation should be as gender-neutral as it is possible to make.