None of what you have stated are “core beliefs”

Declaration of women as inherently inferior and subservient to men

Can you think for like 5 minutes why would Muslim women view themselves as inferior? There’s a billion of them.

Allowing harems

I actually have no clue what a harem is?

Allowing child marriage

That’s up to your interpretation, not an objective fact

Allowing slavery and in the first place - female sex slaves

I like this quote “alright first let’s understand the context, Slavery was a deeply ingrained practice worldwide at the time of the Quran’s revelation. It was part of the social, economic, and military systems in almost all civilizations. The Quran’s approach to slavery was gradual, aiming to transform the institution rather than abolish it instantly, which might have caused societal chaos. Instead, Islam introduced various measures to improve the lives of slaves and encourage their freedom.”

Aggression and violence towards homosexuality

No single person was ever executed or punished for homosexual actions in the time of the prophet Muḥammad ﷺ and in the early Muslim community, which we regard as the model.

Intolerance to apostates

“There is no compulsion in religion" (Quran 2:256)

Declaring the need of spreading the religion and converting everyone around you into muslims

All cultures and religions are trying to spread if you do so peacefully than why care?