I would strongly suggest actually reading the study rather relying on someone else's summary. In particular, pay attention to the reason why she ran the second study and what was actually being measured, namely reactions to this paragraph:
“I disagree with the many people who think that women should be cherished and protected by men. You know I’m strongly against that whole idea that in a disaster women should always be rescued before men. And I really don’t agree with those who say that men should put women on a pedestal or that men are incomplete without women in their lives. There seems to be this popular attitude that women are more pure and moral than men and that women should therefore be treated with greater respect than men, but I think that’s a lot of nonsense.”
The second study found that simply prefixing that paragraph with “I’m a firm believer in equality between men and women. And because of that” removed much of the ambiguity which lead many people to conclude that the author was probably a misogynist.
Beyond that, simply looking at the test is already telling you that this isn't the sweeping result certain defensive men are claiming – it's a single study measuring reactions to a single, somewhat stilted paragraph over the internet in isolation (they used Mechanical Turk to get participants). That doesn't mean that it's not a decent study but it would immediately tell you not to believe the results apply generally to complex real-world interactions where few normal people randomly state manifestos like that and almost everything happens in a context with a history of past interactions which guide the listener's interpretation.