I am not saying that there are absolute right(correct)s in morality, at least not any that I can prove, but that if the basis and justification for some precept of some moral system is false, then that precept is therefore by extension false. this is a completely separate issue from the absolute subjectivity (or not) and by extension absolute inability (or ability) for one person to judge the actions of another person. If there are as you say "certain shared criteria" then that means that any person can use that criteria as a basis for judgement for any other person regardless of culture. They are shared*, they are universal*, and are therefore not subjective. note that what I am saying here is qualified.
Just because you can observe that due to our human nature and the nature of our societies certain shared moral criteria evolve, i.e. can be defined and "described" does not at all necessarily mean that you can presume that they are absolute and it would be a good idea to "prescribe" them. (Look into descriptive and prescriptive lexicography and you will find the same hilarity.... what the "right" way to speak and spell is appears to be just as hilariously controverse as what the "right" thing to do is... but due to the nature of the matter, lexicography can usually be discussed in a much more lighthearted manner, because most of us are not so emotionally invested in the subject... unless you talk to a lexicographer, then you will find fervor and fanatism to match any religious discussion.)
As far as disproving religion goes, what you are missing is that (part) of the moral system could be "right" despite the justification for it being wrong (... why? well because it evolved and survived and propagated itself and obviously also is the basis of a society that doesn't immidiately collapse onto itself). As any judgment could only be passed from another morally subjective position it is frankly outright irrelevant if the religion that the moral framework comes from is true or not.
Let me clarify: Can you imagine a society where killing as many of your neighbors as possible is a basic moral prerogative successfully propagating itself? It's quite easy to conclude that any moral framework developing in human societies has something against concepts that threathen the survival of that society (and if it doesn't it just ceases to exist). That's not absolutism, that's evolution.
One of the most prevalent concepts appears to be "Don't do to others what you would not like to be done to yourself". Of course this may be amended to suit certain societies and religion by defining "others" as being male or believers or whatever suits the majority that is in power, but while modified... the underlaying principle is still apparant: Treat others of your arbitrarily defined peer group nicely or your arbitrarily defined peer group will likely suffer". Just common sense, right?

That's also why external threaths and common enemies are so effective at suddenly making people overcome their religious and ideological differences... an external threath suddenly forces you redefine who your peers are in order to survive.
What you can observe is that religious moral frameworks usually feature rules and concepts that directly advocate strong belief and the spread of that belief (like the concept of "going to hell" as punishment or the more worldly "death sentence" for apostacy in Islam)... that's also evolution, it helps religion to survive. Only ideas designed to last and spread themselves survive. That moral frameworks of stable societies feature certain shared criteria that are benefitical for that kind of society to propagate itself is just applied evolution as well.
Frankly... the whole question of whether morals are "true or false" as an absolute statement is outright missing the point when considering the nature, evolution and purpose of moral systems. It's like asking whether humans are the "right" organism to evolve. I.e. Right and wrong is pointless, what evolved just exists because... well, it evolved in the face of environmental pressure and we understand why it would, given the environment.
If circumstances change so will moral systems (or they will be diminished and disappear: See the current decline of the catholic church in Europe.). But our circumstances being well..... "being human" and "living in human societies" it is only natural that we share some basic moral concepts. (i.e. the ones that benefit the survival of our societies that propagate said moral systems

)
See... when I read a story like the one in above's original post I am horrified, because empathy for my fellow human beings, be they female or male is very important to me. At the same time I realize that the same "empathy" that is a fundemental part of my life philosophy would be considered a fatal weakness by people with a different worldview. Worse... they would happily exploit my empathy for their own ends because from their viewpoint I don't deserve anything else. Both of us are right and wrong depending on the viewpoint and neither of us could imagine changing their viewpoint and for both of us the truth of our morals is self-evident... time for some bloodshed! Empathy? ... but that applies only to my peer group which includes *everyone* ... uh, except greedy abusive ar**eholes!!!

lol.
P.S. From the perspective of an enlightened galactic civilization living in harmony with its neighbors it would be the moral thing to do to contain or end any of our current "human" societies before we get unleashed on the universe at large and cause untold harm to less advanced civilizations with our intolerance, greed and aggressiveness. Minor differences... like Islam or Christianity would likely not even register considering the "big picture".
If you want a more lingwinded and twisted exploration of moral relativity (packaged in an amusing story) just read
http://lesswrong.com/lw/y5/the_babyeating_aliens_18/ . Props to Batutta for first posting it here a long time ago.