I think it's absolutely hilarious how you think christians in australia are actively stopping societal progress (as if the church has any meaningful impact on political discourse and the average aussie christian is staunchly socially conservative), and yet you think muslims, for whom actual devotion to their religion is not at all uncommon, will have no significant cultural impacts on western nations.
Any religion which has power in our political system has meaningful impact on our political discourse. Although we are not a "christian" nation to anywhere near the extent of, say, the US, around 60% of people in Australia identify as Christian (Census circa ~2009 if I recall), and most of our morals and laws are based of Christian values. Furthermore, we have this oversensitivity to religion where we "can't do anything that might upset them" - namely Christianity because of it's prevalence in our society - for example, we can't legalise gay marriage, euthanasia, abortion etc. because it might offend the Christians. As a society we are too familiar, comfortable and sensitive to conservative Christian values, which does inhibit social progress. And because of our heritage stemming from Christian values we place a lot of value on asceticism which inhibits
individual fulfilment (drug and alcohol laws, sex laws such as age of consent and statutory rape).
Now, Islam, on the other hand, is nowhere near as prevalent or mainstream in our society, and because of the fear of "Islamic Terrorists" it is almost acceptable to defame Islam. So our society doesn't really care about Islam as much, and so they have less power. As well as coming almost entirely from immigration and has a very minor role in establishing our cultural heritage.
The Stuart-Mill Harm principle is I think what you're getting that there and yes that should provide the governing basis for our immigration law.
I don't do famous principles usually so I am not familiar with it. But if it agrees with me then I'm sure it's good.