The thing the established order finds frightening about Islam is not violence.
I want to state that plainly because it sounds like special pleading and it is not. Islamist violence is, measured against any serious threat to the Western order, marginal. It has never taken a capital, never toppled a Western government, never altered a single structural feature of the system it attacks.
What the order actually cannot accommodate is the opposite scenario.
A functioning Islamic civilisation. Not a threatening one. A working one: solvent, technically competent, governing well, treating its minorities decently, and doing all of it on foundations that contradict the ones everybody has been told are the only available foundations.
Because the argument for the current arrangement has never really been that it is good. It is that it is inevitable. A working counterexample does not refute an argument about what is best. It refutes an argument about what is possible, and that is a far harder thing to survive.
The collision is not about policy. It is about first principles, and the Western ones are rarely stated because they are not experienced as claims.
The individual is sovereign. The market arbitrates. More choice is progress.
Now the Islamic answers, which are not adjustments to those but replacements for them.
God is sovereign, not the self. The human being is khalifah, a trustee. Freedom is real and bounded, by stewardship, by the rights of others, by obligations to an owner who is not you.
Wealth is amanah, a trust rather than a possession, held under examination about how it was got, how it was used, and what claims others had on it.
That is not a modification of liberalism. It is a different operating system, and the two do not compose.
Three objections, and they deserve better than dismissal.
The first: no Muslim-majority state currently does any of this. Correct, and it is the strongest thing anyone can say against the argument. A framework nobody operates is a hypothesis, not an alternative, and it should be described that way.
The second: the history includes plenty that was not just. It does. Any argument that requires the Islamic past to be clean will lose, and it deserves to.
The third, and the serious one: a framework that subordinates individual desire to communal good is precisely the structure under which minorities and dissenters suffer. Anyone advancing this has to answer it rather than wave at the Constitution of Madinah, and the answer has to be structural rather than a promise of good intentions, because everybody's intentions are good.
Most modern Islamic discourse takes the defensive posture, arguing that Islam is compatible with modernity, as though modernity were the measuring stick and the task were to pass an inspection.
That posture concedes the whole argument before it starts. It accepts that one of the two systems is the standard and the other is the applicant.
The interesting question is the reverse, and nobody in the current arrangement is ever required to answer it. Not whether Islam can justify itself to the modern order.
Whether the modern order, holding the ledger of the last five centuries and the numbers of the last twenty years, can justify itself to anyone at all.