Had I been a muslimman, I would have been able to have sex plenty
This is equal to the unfulfulled conditional (conditional 3)
If I had been a muslim man , I would have been able to have sex plenty
The only difference between the two structutes is :
In the first sentence there is an inversion of the verb had and if is omitted..
The sentence means I was not a muslim man ( but I was a muslim woman), so I was not able to have sex plenty
In the link you provided, The woman thinks that as a muslim woman she did not have the freedom of a muslim man.
She was not able to do what she wanted to do as she was a muslim woman
You can use similar structures in your writing.
Had I been a professor, I would have taught English lessons
Had I been a doctor, I would have treated the patients