There are many interesting ideas to unpack in these memoirs. First, it should be noticed that the writer has a strong thirst for power because she wants to be free from the dominion of how her culture treats her as a woman. First and foremost, her attitude is delightfully entitled, because her being able to do whatever she wants when she is dressed as a man is proof against her culture of their hypocritical standards.
This entitles her to be a public voice, because she comments from the lengthy experience of having been in a man's clothing. She realizes that, if you're a man, no one cares who you have sex with, and no one cares what sorts of drugs you might like to take to get high. The assumption is that of course men will live the good life, which makes Eberhardt perfectly aware of the culture's maladaptation to religion. The religion doesn't compel the religion of the men; only the women.
That doesn't mean she disagrees with Islam! She still reads her Quran and prays, but at the end of the day, she doesn't trust the mosques to tell her what to think or how she has to be, because of course behind closed doors, she sees the same men who act religious, taking drugs and having fun. She is not fooled by the organized religion, but even although she is free, she still keeps her faith nearby, never quite leaving it aside.