The popular narrative from mainstream media and a lot of feminists is that conservatives are more sexist towards women. Well, this isn't true. But let's look at how you define sexism. There's two types of sexism: benevolent and hostile sexism. Benevolent prejudice is a form of prejudice in which we cherish a group of people in a patronizing way that still marginalizes them, often because we're infantilizing them or treating them off their identity instead of the content of their character.

Are conservatives less egalitarian?

Believe it or not, conservatives and liberals actually are egalitarian in their own unique ways. For example, conservatives treated the success of black and female athletes vs white or male athletes comparably, whereas liberals promoted the success of black or female athletes more. Liberals are much more likely to support affirmative action or allowing people into certain institutions or organizations because they're black or because they're a woman, whereas conservatives advocated allowing people in equally as each other. Liberals judged information or passages that portrayed women, black people, or Muslims negatively more harshly compared to passages or information that portrayed men, whites or Christians that way, whereas conservatives treated both comparably. People were also more likely to judge a study that showed sex or racial differences showing whites or men doing a better job at something more negatively, especially liberals, whereas conservatives treated studies showing pro-female/black sex/race differences and studies showing pro-white/pro-male sex differences (eg: men/women are better at being president or whites/blacks had higher IQs) more comparably. Liberals also were more likely to dumb down their language when talking to blacks vs whites but conservatives spoke to blacks with the same language they did to whites.

Liberals, in other words, engage in more benevolent racism whereas conservatives are more hostilely racist, which is why they lack empathy towards black people's struggles more. Affirmative action? That's tokenism. Dumbing down your language when talking to black people? That's infantilizing. Conservatives tend to support hierarchy or maintaining how things currently have been for a while, which is why they don't mind unequal outcomes for groups of people, whereas liberals value blacks and whites having equal success in life. Nonetheless, this doesn't mean liberals are more egalitarian.

It could be liberals prioritize equal outcomes for men/women, blacks/whites, straights/gays, etc., but believe unequal treatment is vital (for some time) to make outcomes equal, whereas conservatives (except the alt-right, who are genuinely anti-equality) prioritize equal treatment, but view unequal outcomes (for a time) as an unfortunate side effect. They might complain about unequal outcomes and how reverse discrimination is now happening because of it, but they eventually get used to it, which is why so many now support gay marriage. Liberals, on the other hand, want equal outcomes, and won't stop unequal "affirmative action" treatment until it finally happens.

Are conservatives more benevolently sexist?

Probably not. It is true that conservatives score higher on some sexism scales used, but most of it isn't "i hate women" statements, but statements that show conservatives believing sexism doesn't exist anymore and believing in traditional gender norms such as men are better leaders, or women are better nurturers, or conservatives not prioritizing equal outcomes for men and women. Conservatives aren't more sexist though. Here's how:

Most sexism towards women is benevolent sexism, but the media acts like hostile sexism is the norm. I already explained it in that thread of mine, which research showing that people have more positive feelings towards women and negative feelings towards men, even in traditional countries. It's not a reaction to patriarchy, but due to gender roles such as women being harmless, kind, nurturing and in need of protection, and men being antagonistic, harmful, scary, cold, and are supposed to man up and handle their issues on their own. Most gender roles about women were found to be due to social norms, not hatred of women. In fact, feminists are highly benevolently sexist themselves. In fact, leftists do engage in a lot of benevolent prejudice. That's why feminists portray women as damsels in distress all the time, prioritizes female victims of crime more than male victims even if male victims are the majority, portray any violent woman as the automatic victim, and reinforce modern gender roles about women (e.g.: you need to go to college, have premarital sex and not marry or have kids until you're at least 30). That's why feminists dismiss old gender roles which aren't even the norm anymore such as virginity, marriage and kids, not knowing these norms are gone because they live under a rock, and instead normalize education/career and having premarital sex, which is actually normalized by the establishment these days. Feminists also portray men as criminals, evil, violent, womanizers, always suppressing their emotions, and never the victim and always the antagonist when a woman attacks or mistreats him. Read these two linked threads. Feminism reinforces the attitude about men and women society always had, but with a woke twist. Liberals are benevolently sexist towards women just as much, but in a more woke way.

Are conservatives more hostilely sexist toward women?

No they are not. This study measured people's hostility or liking towards certain groups of people between liberals and conservatives. Although conservatives scored higher on the modern sexism scale, this didn't prove they were more sexist, because conservatives might not value equal outcomes as much as liberals do, so they might think women aren't oppressed anymore or might believe in traditional gender norms about men being better leaders or women being better nurturers. The modern sexism scale didn't even appear hostilely sexist, but more based on being comfortable with the way things currently are, and belief in traditional gender norms. I read it. This explains why modern sexism wasn't particularly negatively associated with positive beliefs towards women. It looks more like benevolent sexism. Conservatives however, did not have a lower positive attitude towards women nor men, and viewed them both equally. In fact, hostilely racist people more likely to have more negative beliefs about women. Conservatism wasn't even associated with a greater liking towards men.

https://preview.redd.it/x15yjddd1m8b1.png?width=746&format=png&auto=webp&v=enabled&s=a8d63447342ce00bb1100142026f4611e09cf84f

Although liberals had a slightly more positive opinion of women on their rating scale, it wasn't statistically significant. Conservatives had slightly more positive opinion of men, and viewed women slightly better than men, but liberals viewed women much more positively than they viewed men.

https://preview.redd.it/rf09czxc2m8b1.png?width=742&format=png&auto=webp&v=enabled&s=0442c80b9490de38cb83221e8882a3de68ff5313

Now, conservatives did score higher on hostile racism, but this is the only racism that gets attention. Liberals are less hostilely racist towards people of color, but more benevolently racist. Conservatives also were found to rate men and women equally intelligent, but liberals rated women as more intelligent than men, and rated them as more intelligent than conservatives rated them, but conservatives rated men and women equally intelligent.

https://preview.redd.it/sry59ff43m8b1.png?width=778&format=png&auto=webp&v=enabled&s=b2c7b185cf6c37a0cabe0f17e789e05cf73ae0fd

Another study found a similar finding. Republicans and Democrats rated women very favorably, and didn't differ from each other about it. Republicans rated men and women equally, but Democrats rated men less favorably than women.

https://preview.redd.it/agn2a5zs4m8b1.png?width=681&format=png&auto=webp&v=enabled&s=44834b095efd3eacf7e74a8a3f05564d5181aa77

Another study found that conservatives did not show more negative feelings toward women, and if anything, liberals did slightly more, but liberals showed more negative feelings toward men than conservatives, and much more negative feelings towards Christians, elders, rich people, white people, etc. What they found was liberals weren't actually tolerant, they, like conservatives, just as less tolerant or positive toward people who defy their interests.

https://preview.redd.it/atb6v65j5m8b1.png?width=753&format=png&auto=webp&v=enabled&s=1c84e8bd74948b4b12e13e33112c83d148123a47

But of course, the hostile sexism scale can't measure hostile sexism among conservatives because a lot of it has to do with anti-feminist beliefs, which doesn't equal hatred of women. It could be conservatives might score higher on a benevolent sexism scale, but liberals are just as benevolently sexist, just in a more woke, subtle way and thus, liberals might have a self-unawareness and social desirability bias. That's why feminists might score low on the benevolent sexism scale, even though they are the epitome of benevolent sexism, which I discuss in a thread I linked above.

Conclusion

It doesn't appear that conservatives are more hostilely sexist or benevolently sexist toward women. It is true that hostilely sexist people are more likely to have voted for Trump (which I read in other statistics), but that doesn't mean conservatives are more hostilely sexist, and is a just a post-designation fallacy. Hostilely sexist men do believe in more traditional gender norms about both men and women, but these guys aren't necessarily conservative in general, and thus could be liberals. For example, there could be hostilely sexist men of color in the U.S., but they clearly aren't going to be right-wingers.