Lets just agree to disagree.
Achamenid Empire was multiethnic and broadly tolerant to different faiths, although Zoroastrianism was the official state religion. But Achamenid empire was a ethno-cultural-linguistic empire. It was not a IDEOLOGICAL empire like Islam.
The Caliphate became decentralized after Abbasid revolution.
The caliphate was a PURELY IDEOLOGICAL empire, open for anyone to become muslim and accepted as fullworthy citizen simply on observing the Shahada. That means anyone regardless of skin color, ethnicity and culture could become a muslim, without abandonding the aforementioned identities. Even non-muslims could become a citizen, but they were characterized as dhimmies, which simply means protected. They were extempted from military service (which was mandatory in theory for every male muslim) but had to pay a poll tax.
Concerning the modern western liberal democracy, there is a need for defining what that really means. Because i imagine that you are mixing the post-modernism ideology with the term liberalism. Those two terms had nothing to do with eachother until recent 60 years or so. Classical liberalism has very much in common with Islam. In fact the western world didnt become postmodernist and LGBT oriented until recently, wich is mere a blink in its almost 1000 year long history.
What i am trying to explain to you is that its very hard for modern western world to lay out what is its own real identity. What makes western world western? Until recently it was no question, you had to be some form of christian and white. Today its usually respect for democracy and atleast sole form of post-modernism. That is also the reason many westerners feel alianated when they meet a person of color, even though the colored person may be educated,tolerant towards sexual freedom and respecte democracy. Historically you had to be caucasian white and christian or else your life could be in danger. That was never the case in any islamic society. The major red line in islamic society was always blasphemy, if you could steer away from PUBLIC blasphemy, you were accepted as a islamicate citizen.
I could go on and on as this is a field which is of major interest for me. As mich as i would say it has changed my life and world outlook forever.
This is my last but long post(excuse me) on this topic, which tbh is totally offtopic