I disagree strongly....Kingdom of Heaven was very religious, it was slightly biased toward anti clericalism, but given the subject matter that is to be expected given the reasons that Pope Urban actually had for the Crusades to begin with and Pope Alexander III issues with legitimacy.....if you look at the Characters they are all religious to one extent or another....
There are plenty of redeemable Christian Characters....Balian for one, the Knight Hospitaller for another.....
Historically the film has some factual issues....Balian's bloodline and heritage for one, and with regard to your concerns, the Patriarch of Jerusalem is grossly misrepresented as Patriarch Heraclius was probably the opposite kind of man than the negative way he is portrayed in the film (but overall it is a good representation of the period and piety of the time.....)
Another good example of the piety and impact that religion had, but the corruption within the Church that led to anti-clericalism among the Nobility especially is Pillars of the Earth.......
Don't confuse anti clericalism with anti-religion....they are not necessarily the same thing. Remember the Word may be from God, but the Church is from Man........