I don't really understand the premise. The idea being what conflicts there are between Christian morality and the Secular one? Well, those two things are really not comparable anymore, as the latter has gone off-kilter into the vague, or the absolutely relative (as you yourself intimate).
It makes one think of the young cadres raised in the Soviet Union say, that would consider the forceful liquidisation of the Kulaks as a moral good, or the Nazis killing the Jews. These are not moral actions I would think, but are the prevailing societal model there. In similar vein, slavery prior to its abolition by Christendom, or Infanticide in ancient Sparta or Carthage, or human sacrifice in Meso-America. Either we judge these dispassionately as evil actions, or we accept them as good to those societies in the relative model - which renders moral precepts merely my Jingoism above yours, and thus negates any value the concept holds. Even if wectake some Social Darwinist approach, you would still essentially just assume your side more right to continue and live on account of being yours.
Either things are intrinsically Good or moral, or the concept actually doesn't exist and anything is as good as anything else. As far as I am concerned, you either have to assume that something is axiomatically good, that feeding a child better than killing it, and that immediately implies a standard to which you can reach. If you try and ascertain that standard, whether it is by Natural Law or Revelation matters not, you are still assuming a Rational base for morality that is not just a relative hodgepodge.
I don't think Christianity, or anyone, has really budged at all. History is long, and we are still in that phase that follows the start of the decline of great civilisations, where much is turned on its head. No one is okay with getting divorced, most young girls don't want to sleep around (bit different for the boys, of course), and even things like homosexuality or abortion or euthanasia we see the erection of euphemism. If you can't mention the thing in plain terms, you are erecting smoke and mirrors to deflect. I don't think there is a clear idea of any morality in the secular world, only the detritus of a decaying Christian fabric. The Christians that still cling to this have forgotten that we are in the world, but not of it. Christianity will move a bit counter-culturally, but time is long. Aberrant societies, with weird ideas as I mentioned earlier, existed before and we are just creating another one like it - the correction will come, either by human hands or by the Divine. I mean, the optimum functioning of humans by the evidence, cold hard data, shows monogamous male-female family units with close family ties are by far the most succesful and commonplace human model - by simple Darwinism, a correction can be expected. I wouldn't put too much stock in just our moment of time as somehow special.