I really don't want to be the voice of feminism anywhere. However, I'm willing to be the voice of Twilight apologism, so:
Bella is presented as an accident-prone, self-sacrificing human, frequently putting herself in legitimately dangerous situations for poorly thought out reasons. If you read into the dynamics of vampire pairing-off, which I think is sufficiently obvious that I poured it wholesale into my fic, this is sufficient for Edward to go a little nuts. Gender needn't enter into it. He's a vampire, nigh-indestructible, and he's irrevocably in love with someone extremely fragile who will not stop putting herself in myriad situations that he evaluates as dangerous.
He should just turn her, of course, but he has his own issues with considering that a form of death, which aren't addressed head-on in the canon at all; he only turns her when the alternative is immediate death rather than slow gentle death by aging. So instead of course he resorts to being a moderately controlling "rescuer" - of course he does things like disable her car so she can't go visiting wolves over his warnings. Wolves are dangerous enough to threaten vampires, and Edward lives in a world where violence is a first or at least a second resort to everything. Bella's life is more valuable to him than it is to her, and she shows it. It's a miracle he didn't go spare to the point of locking her in a basement, given that he refused to make her a vampire. (Am I saying Bella should have meekly accepted that he wanted to manage her life? No, I'm saying she should have gotten over her romantic notion that Edward needed to turn her himself and gotten it over with. After she's a vampire in canon, she's no longer dependent - emotionally attached, definitely, and they're keeping an eye on her to make sure she doesn't eat anybody, but she's no longer liable to be killed in a car accident or anything and there's no further attempt ever to restrict her movement. She winds up being a pivotal figure in the final battle, which no one even suggests keeping her away from.)
Note that gender has nothing to do with any of this. The same dynamic would play out with any unwilling-to-turn-people vampire who mated to any reckless human. It's fully determined by those personality traits, this vampire tendency, and the relative fragility of humans. So, to hold that this dynamic makes Twilight anti-feminist is to hold one of the following ridiculous positions:
the mate bond as implied in the series is intrinsically anti-feminist (even though there's nothing obviously stopping it from playing out with gay couples, or female vampires with male humans)
it was somehow irresponsible to choose to write a heterosexual human female perspective character (...?)
it was antifeminist to write a vampire love interest who wasn't all for the idea of turning his mate immediately (it is completely unclear how Edward's internal turmoil about whether turning is death has anything to do with feminism in the abstract, so his individual application of this quandary to Bella can't be much more so)
Other feminist accusations fail trivially. Bella doesn't get an abortion. So? She doesn't want one! It's called "pro-choice", not "pro-attacking-a-pregnant-woman-because-your-judgment-overrides-hers". Etcetera.
I don't credit Stephenie Meyer with enough intelligence to have figured out this line of reasoning. I think it's most likely that Meyer created situations so that Edward could save Bella, and due to either lack of imagination or inability to notice, the preponderance of dangerous situations (and especially dangerous people) ended up very high - high enough to give smarter people ideas like violence is just more common in that world.
That said, my views on Twilight are extremely biased by my social group.
I've often had half-finished LW post ideas and crossed them off for a number of reasons, mostly they were too rough or undeveloped and I didn't feel expert enough. Other people might worry their post would be judged harshly, or feel overwhelmed, or worried about topicality, or they just want some community input before adding it.
So: this is a special sort of open thread. Please post your unfinished ideas and sketches for LW posts here as comments, if you would like constructive critique, assistance and checking from people with more expertise, etc. Just pile them in without worrying too much. Ideas can be as short as a single sentence or as long as a finished post. Both subject and presentation are on topic in replies. Bad ideas should be mined for whatever good can be found in them. Good ideas should be poked with challenges to make them stronger. No being nasty!