Some IL background for you folks and some of my two cents.
From the perspective of true democracy, the women's rights people are correct. This has to be said. Just because halacha may (may!) make this untenable doesn't mean that it is lawful to force women to travel on the back. As such, when it comes to public transportation, any forced seating arrangement is bound to make anyone who doesn't believe in the Torah as Hashem's final Word forever absolutely outraged. And this is what many Chiloni ladies feel.
The halacha aspect is too nuanced to do justice, but al regel achas, it may be that any power Charedim have to force the issue should be used, but even if this was universally accepted among the poskim, it is not applicable in every situation - that would depend on how bad the transgression being prevented is. Should we use our political power to prevent public transportation on Shabbos? Should be have separate walking areas in the public domain (at least where we live)?
The Chilonim are, by and large, unable to differentiate between a worldly Charedi who asks (nicely) for something out of halachic preference versus a Charedi who believes that the Torah should be forced on everyone else to the largest extent possible. And after a while dealing with the latter, they may lash out at the former in advance. I am not apologizing for them, but this IS a world in which nuance is being thrown out the window and everyone moves to the extremes. So it goes.
Now a bit on recent IL events. For years, Yeshivas Mir paid Egged for use of public transportation buses. These buses had real line numbers and schedules. Then the government (maybe just Y-m, I don't know) decided it wasn't legal to use such public buses in a way that who was allowed to get on was limited, and the Mir had to switch to private charter (at much greater expense). There are, however, still places that run buses to yeshivos. When a lady tries to get on, the people on the bus say the bus is private. I don't know if this is true. Again, if the bus is technically public and this is a democracy (it isn't really but it is somewhat democratic), the lady is right and the men are wrong. (To be clear: mitzad democracy.)
Again, mitzad democracy (and this is the perspective of these complainers), a driver should not tell a girl she isn't dressed enough and cannot ride. (If you aren't going to pass a law defining public decency, you can't decide anything is indecent.) Yet this has happened in the last few weeks.
It shouldn't be verboten to ASK. But so many have not - they have DEMANDED. And because of the (WRONG) Chiloni perspective, they are tired of it. None of this excuses Neria for reasons that have been articulated well enough by everyone else.
On the other hand, when (as I have noted elsewhere) the Supreme Court prohibits a Charedi cultural event of some sort - funded by us, attended by us - because of separate seating, that is inexcusable. We should have the right to do as we wish among our own.
Also, the Torah does not believe in democracy nor tolerance for averah. The only reason Jews were into democracy was because it was better than what came before it.