There’s literally a movement within MAGA to repeal the right of women to vote. Yes, I absolutely believe that the misogyny is present in today’s GOP. Further, multiple polls and other research studies have found that a significant number of voters in the US does not support the idea of a woman for president. Here are a few references:

https://journals.sagepub.com/doi/10.1177/1532673X251369844

https://thehill.com/homenews/campaign/4782780-americansready-female-president-dipping-survey/

Anecdotally, Michelle Obama recently observed the same thing: https://thehill.com/homenews/campaign/5607777-michelle-obama-us-not-ready-woman-president/

And if you combine her observation with the GOP views on women as president reflected in this pew research poll (notably “Republicans (86%) are twice as likely as Democrats (43%) to say it is not at all or not too important if they ever see a woman elected U.S. president”), I think there’s ample reason to believe that a Republican candidate for president would struggle to gain support from a statistically relevant group of voters.

And no, I do not think that Clinton And Harris lost only because they’re women. I did not say that at. Evidence suggests that misogyny was one of many factors, though.