Muslim here, so I can reply to the question as opposed to someone who only knows about Islam from what the media or the predominant islamophobic content we find on the internet tells them about what to think about it. When you have a question about the Mercator projection, you normally don't go to a flatearther...
She was a theologian, so she studied religions and left Islam to the last, which she ended up accepting based on the scripture once she studied it.
As to the stance of Islam with regards to being gay, the sexual act is forbidden as in one should abstain from actually doing it. Thinking about it or having the desire without acting upon it is not considered a sin. There are punishments in the Islamic law for when a person has been seen by 4 eyewitnesses performing same-sex fornication. To my knowledge this has never been followed through by a judge in the Islamic state of the 4 caliphates as the prerequisites are, intentionally, hard to come by: spying invalidates the testimony, the act should take place out of the privacy of their home etc. So it's really if the person is doing it in the open... Now I don't speak about what western media uphold as THE Islamic states such as Iran and Saudi Arabia which are not following strictly the law (and its prerequisites). They have laws that are quite... theirs. Also being gay and being Muslim are not incompatible, since a Muslim is always striving to submit to the divine will and overcome one's own desires. As long as a person is sincere and keeps repenting for his/her eventual shortcomings and never disbelieves in God they remain a Muslim.
About why would a feminist accept Islam, if you study it you'll know that it is not misogynistic (ie. considers women as lower than men or is hateful against women). Rather it has a fundamentally different and more factual stance: women are psychologically and physically different from men. So it is about equity and not equality: women do some things better than men and men can so some things better that women; women desire different things than men. To each their role in a family and in society as a whole. Both are honoured in what they do, and you'd even find women are even more honoured, revered and protected.
"Openness" has less to do with sects and as another person commented is more about the society. Muslims, +90% of which are Sunni, have the same source of law but the differences do not come from the religion but are societal.
The religion tells both males and females what they should and what they should not do. Most of it is the same, some of it is different depending on the gender.
I genuinely don't see how the above is misogynistic.
I encourage you to study it. Find reliable Muslim sources who know what they are talking about and increase your knowledge. I may recommend sine YouTube channels like Muslim Lantern or Dawahwise.