Both Aristotle and Plato's ideas were based around the assumption that 'gods' existed. I don't think the same was true of Confucius.
And yet Nestorians in China during the Tang dynasty cited Confucian scholars.
Funny how that works.
Again, the crucial thing to remember is that, in the Medieval context, the religious authorities took each other seriously as learned academics and credentialed experts in what they regarded as a rigorous field. That does not mean they agreed with each other, far from it, but it does mean that simply suggesting that theological issues would have a natural, subjective diversion along cultural lines would have been anathema.
(On a sidenote, I think Aristotle and Plato would object to being characterized as "assuming" gods exist, as they saw themselves as demonstrating that a god or divine power must exist, and other Medievals also did not view themselves as assuming that a god or gods existed.)
