Oh. It's a hot mess today in Democrat and mainstream feminism boards because emotions are high and Greene is the devil trying to kill trans people. They aren't necessarily wrong. However, the devil is really in the details...and in the consciousness of too many people's brains.
Greene is, by so many measures, an awful, awful human being. You don't have to be a leftist to find her behavior repugnant. Her attack on this bill is a fucking death knell to any reasonable changes that could have amended the act and changed the definition of sex.
Nobody wants to be seen as an ally of Greene. Now, instead of any reasonable compromises (like ensure no discrimination in employment/housing/education for trans people while also ensuring sex-based protections for girls and women), this poorly crafted bill will likely get passed in the House as is. Then, reasonable Senators may feel that any opposition to this bill will taint them with the likes of Greene, so it might pass in the Senate. While I don't see that as a given, I just see that Greene has made it much more difficult to argue that there is a perfectly balanced, non-religious and good reason to vote against this bill.
Once again, the voices of women and girls are drowned out by the crazy right wing conspiracy nutters and the crazy TRA wing zealots. Nobody with any sense feels safe enough to speak up.
Too many Americans are educated by religious institutions...it has distorted our civil discourse and hindered our reasoning abilities. This can be seen from comments on both sides of the debate like these: "God loves all the genders because he made LGBTQA people and they are perfect in his eyes."
"God only made two genders and it is a sin for a man to make himself a woman and for a woman to make herself a man." 
Seriously...many people in the US think like this and you just.can't.talk.to.them.