Personally, I thought having a girl hero is a cliche these days, and I think that's what the people who are up in arms about it are reacting to. "Why are you putting your politics in my game even if it is a relatively harmless gesture? It's tasteless and you only did it to pander to some people whose opinions I don't very much agree with!"
Culturally a girl just doesn't fit into that role, so it feels disingenuous. And the hook hand thing? Wtf was that. The whole trailer was a messy headache of fast cuts and dirtied camera lens shots, it was hard to watch, going past their transparent attempt to titillate a certain audience.
I do like how it accurately captures what is different from a BF than a CoD. Vehicle combat, large maps etc, so in that sense, the trailer felt honest.