That isn't what the study data says!

They actually did five different studies which don't even fully agree with each other on the questions which overlap.

For example, for Study 4, they found that: "feminists were slightly less positive toward men relative to nonfeminists (H2)" (See Table 4; p = 0.024.) They also probed ideology, and found that "As expected (H3), all types of feminist ideology, except liberal feminism (p = .217), were negatively related to explicit attitudes toward men (all rs between −.31 and −.11; all ps < .041)."

Then they did Study 5 and found the opposite thing, which they only partly explain: "feminists reported slightly warmer attitudes than nonfeminists (H2). Further exploration of a gender/sex interaction F(1, 1828) = 13.58, p < .001, η2p = .01 showed differences between feminists and nonfeminists were only significant for male participants". But that isn't consistent with Study 4, and anyway, they make the classic mistake of conflating "not statistically significant" with "no difference". If you look at the supplementary materials, in fact, the Study 5 female feminist average liking of men is higher, but non-significantly so, than the Study 5 female non-feminists. This makes it impossible for two studies' results to actually concur. They don't examine other factors, but my first guess would be that if it's a real effect (not some sort of selective effect due to improper sampling methodology), it's due to age, because Study 5 includes older people. (They didn't regress against age.)

So we can conclude quite confidently that they don't have a very good handle on what's going on here; it's hard to tell whether there are methodology problems, age differences, or what. Social science surveys are hard to get right, and despite their declarations, they haven't done it well enough to make those sorts of conclusions.

Anyway, your bolded statement "Feminist women did not have a lower opinion of men" just isn't supported by the data. In Study 4, they did. But more importantly, because the results aren't stable across studies, all we've really learned is that we haven't learned as much as we would like about this. (We've put bounds on how much lower the opinion could be.)

However, what they do seem to have shown pretty convincingly is that everyone thinks that feminists are way more negative towards men than they actually are: "Further, relative to feminists’ actual warmth toward men participants as whole substantially underestimated women feminists’ warmth toward men. This error was committed by feminists and nonfeminists alike. We then examined, for the first time, participants’ understanding of the mechanisms underlying women feminists’ attitudes toward men. As predicted (H7 and H8), and shown in Table 5, participants overestimated women feminists’ perceptions of threat and underestimated their perceptions of gender similarity. This pattern was evident even among feminist participants for threat."

If you dig into the actual numbers, there is some support for your claim that "Anyone who’s spent any amount of time with feminists as a group knows that we don’t hate men — we just hold them to a reasonable standard." Feminists' perceptions of feminists are closer to the reality. But familiarity isn't enough; that only explains about half the discrepancy between perception and reality.

The authors' ability to reason through their own findings is also kind of disappointing. They sometimes make basic errors in interpreting what statistical results mean, and draw conclusions that are consistent with, but are not the only thing consistent with their data (e.g. your last quote from them is not the only interpretation that's consistent--they apparently didn't control for just having a positive personality, for instance). In a case like this, you really have to read the data for yourself, and draw conclusions yourself. If you can...but...with your background in physics, you should possibly be equipped to?

Anyway, it's a good thing to bookmark if you want to document that #NotAllFeministsHateMen. Or that #FeministsDon'tHateMenAsMuchAsYouOrTheyThink.

But the study documents that stronger agreement with more ideologically intense feminism does seem to correlate with poorer views of men, so it doesn't rule out that intense, committed, vocal, non-(classically liberal) feminists do actually have a worse-than-neutral view of men.