I have seen the show and read excerpts from the books (such excerpts are fairly easy to find on the Net). I also have read that, yes, GRRM is a lapsed Catholic and now professes to be either an atheist or an agnostic. I am sure that, by itself, would make his works taboo for some.
However, I actually find GRRM to be quite fair in his approach to religion, unlike, say, a Phillip Pullman. It seems fairly obvious that the Faith of the Seven is modeled on the Catholic Church, the idea of a God with Seven Faces is very similar to the Trinity, the Seven Pointed Star as a symbol of this God is similar to the Shamrock, and the structure of the Faith is certainly very close to Catholic ones; their priests are called Septons and the leader, the High Septon, is elected by a Council of Most Devout in the same way the Cardinals elect a Pope, while their nuns are called Septas.
(And much like Christianity, the Faith started in Essos, which is certainly modeled after the Middle East, and spread to Westeros, modeled after medieval England/Europe, but essentially died out in Essos itself, somewhat similar to how Christians are now a minority in the Middle East.)
Though interestingly, although portraying Westeros in general as a very patriarchal society, GRRM chose to depict the Faith as a trifle more egalitarian; Septas are on the Council of Most Devout and take part in electing a High Septon, and of the Seven Aspects, three are female (Mother, Maiden, Crone), three are male (Father, Warrior, Smith), and one is asexual (The Stranger, who is the Death aspect of the god).
Now, GRRM does show corruption in the Faith equivalent of the Vatican during the story, as the first High Septon we meet is described as fat and corrupt, and is torn apart by an angry mob during a bread riot; but the second is described as a devout man, though a weak-willed one; the third is a firebrand reformer of humble origins. Some individual Septons and Septas are presented sympathetically, while others are not. But I didn’t get any sense that “all members of the Faith are corrupt and insincere”. One of the morally questionable characters who has committed atrocities, later winds up becoming the equivalent of a monk after a near-death experience, and this seemed to be portrayed as a positive development.
As for how the religious lives of major characters are depicted, whether of the Faith or of other religions, GRRM depicts people with many shades of religiosity; the only real atheist I can think of, (at least at the start of the story) is Stannis, but he does have sympathetic reasons for his disbelief, as when he was a child, he prayed for his parents to be saved from a shipwreck but they still drowned.
Tyrion is depicted as a worldly man who doesn’t pay much attention to religion except in terms of the political aspects of the Faith, but I don’t recall him ever actually denying a belief in God. (The same is true for Jaime, Cersei, and others who are very secular in their outlook but don’t seem to actually reject the concept of the divine either.) Catelyn and Davos are depicted as sincere believers of the Faith but it’s not presented as a bad thing at all. (BTW, there is a BIG difference in the TV and book versions of Davos in this, the TV version is an atheist, but he is a believer in the book.)
Of course there are religious fanatics depicted in the books as well, yet Melisandre, the Red Priestess, and Aeron Greyjoy, a priest of the Drowned God, both get POVs and are surprisingly sympathetic in them.
Now, while SOME fans of the books are atheists themselves and claim “the Gods are depicted as false”, I think the events themselves leave room for open-mindedness. Prayers are not always answered, but sometimes are in mysterious ways.
Certainly, the books do have explicit sexual content (though many of the scenes are actually quite brief and vague) and this may pose a problem to some, but I didn’t find the depiction of religion to be that offensive.