Maybe the problem is that you cannot consider the possibility that Islam IS compatible with modern liberal society.
Yes I started with that presumption and then once I actually read about Muhammad, and read about Islam, THEN I changed my mind. Islam is not compatible. It is incompatible because it forces barbaric and primitive laws, beliefs and prejudices based on a book. And the book cannot be questioned and the prophet is beyond question and is also
https://wikiislam.net/wiki/Uswa_Hasana
Criticise any of it and you are to be killed. They never had a reformation and I dont think it's possible for them to have a reformation. It would be blasphemous to criticise or change any of it.
Muhammad was a paedophile. His favourite wife was a 6 year old. He was 52. She was 9 when he started raping her but he was abusing her from the start. Lookup "Thighing". He also liked to suck on her tongue. Not only this but Muhammad had slaves. We even know most of their names. He raped and he killed. He killed thousands of people. He beheaded every male in an entire tribe. 600-900 jews. He and Aisha sat and watched the beheadings. It took days. They took the females and young boys as slaves. The women and young girls became sex slaves. The older ones they sold to buy weapons and horses. Muhammad was a violent, ruthless warlord who dominated and murdered everyone who got in his way. He was eventually murdered by one of his own slave girls. She poisoned some mutton. She reasoned that either he was the prophet and god would save him. Or he was just a man and he would die. He died a few days later. Oh and he also killed people for writing poems about him. Including one of his slave girls.
And yet
"In Islam, the Prophet Muhammad is known as al-Insān al-Kāmil (the perfect human) and uswa hasana (an excellent model of conduct)."
Do you see what the problem is here?
Maybe you should read about Muhammad and think about what you are defending.
This is a good place to start
https://en.wikipedia.org/wiki/Muhammad#Life
and also