IMHO there were two key factors: one, the broadening of new atheism to critiquing religions other than evangelical Christianity, Islam in particular. That gave cover for Western chauvinism, imperialism, and “cultural Christianity” as fighting Islamic repression.

Second, for a good chunk of the movement, new atheism didn’t erase anti-feminism, it just gave it a new veneer. They centered it in pseudoscience rather than religious doctrine. What made this tricky and not readily apparent is that, at least initially, most of those misogynistic new atheists played a self-congratulatory “I have rejected religion ergo I’m one of the ‘good guys’” tune.

The first major public drama that exposed this was elevatorgate; there was some secular/atheist conference where a female attendee had an uncomfortable encounter with a male attendee in an elevator. After the conference, she made a blog post about it saying, guys please don’t be creepy. Now while there were plenty of people who agreed with her, there was also a vocal group that attacked her for it (not surprisingly, the latter included Richard Dawkins).