Whether you have any formal studies to back you opinion or not, you can still give some evidence. For example, I used the fact that in neither the Byzantine Empire nor Czarist Russia did Christianity produce all those things we cherish in Western Civilization. So, perhaps you could site something in Western Civilization that you think wouldn't be there were we not a Christian culture.
Tim, you are picking and choosing a bit here, and I think that's a mistake. Christian influence on Western Civilization isn't debatable: it is imbedded in the cultural heritage. The key word is "Western" and therein lies the once again obvious point that Christianity varies in practice.
The profound split (and IMO the great tragedy of Christendom) between the Latin and Greek churches in 1054 (which of course had been percolating for some time) informs how people categorize East and West, even into the Cold War. (Plenty of the old "you aren't the right kind of Christian" bun fights there, for centuries. See also the fun Croat/Catholics had at the expense of Orthodox/Serbs during WW II, Ustazi, etcetera.)
When you say "ours" who exactly are you talking about?
Or do you think that Christianity's influence is no longer needed?
By whom?
What do you think will or can replace it?
Thus, neither the separation of ecclesiastical and temporal powers and the rise of representative forms of government in Western Civilization owed anything to Christianity
Other than providing a set of common cultural assumptions (about which people of course quarreled) no, no influence at all.
Your assessment does not seem very accurate. Based on some recent reading I did on the relationships between Carolingian, and later HRE, imperial courts. The Defenestration of Prague, for example, sixteen hundreds ish, was in a large part informed by the clash between where and when Church and State authority was valid. (See also the Guelphs and Ghibellenes as pivotal disputes between Church and State well before the Enlightenment.) I can offer you "render unto Caesar" as a root philosophical underpinning of the separation between Church and State, but quite frankly, I don't think that stands up too well, nor do I think it was the critical meme behind it.
The other point about Western Civilization that your OP didn't address is the Reformation, a profound influence on Western thought, and for my money a necessary precursor to the Enlightenment, and from that the eventual attempt to empower the citizen. Without that necessary cultural step, no Protestantism, and thus no cultural philosophical basis for the American Experiment, part and parcel of which are freedom to worship as one pleases, or not at all, and the explicitly anti-Papist (and at the same time Anti-Anglican) doctrine forbidding an official state religion. (Memory foggy, but "How the Scots Invented Western Civilization" is a fun little romp through how patterns of philosophy and thought emerged from the Kilted ones).
Tidbit: some European countries still apply tax revenue to churches/cathedrals (Italy, France, Germany I think, I'd have to check). This is IIRC done as cultural/heritage maintenance, or perhaps, more cynically, as a way to keep attracting tourist revenue. Is that separation of church and state? Is that doctrine universally European?
Second Tidbit: IIRC, Napoleon III was the last Emperor in Europe who one could call "defender of the faith" from the Pope's point of view.
Last bit: without the American petri dish in which the European ideas were played and experimented with, I am not convinced that European Deomcracy would have arisen, although the English Parliamentary example might eventually have spread anyway, due to proximity.
DR