I have had this thought in the context of my being unable to relate to any character I have ever seen on TV. It's not that there's a lack of characters on television identified as Muslim (in fact, there are far more than the proportion of Muslims in the United States would suggest), but it appears to me that all of them are shown to be irreligious or in some significant way non-practicing. Maybe the intended purpose is to humanize those characters in the way that the writers know how, but its effect is to render those characters unrecognizable to me.
You see something similar in terms of the paucity of Mormon characters; there would be no way to guess from American non-sports television programming that there are as many Mormons in the United States as there are Jews. The sense I get is that for a character to be religiously secure forecloses on a great deal of dramatic potential and does not add anything useful in exchange.
That gets to the question of why it might be that religious characters could be difficult. My notion here (and this is speculative even compared to everything else) is that the sort of person who thinks in a serious way about the moral questions on which religion might have bearing is unlikely to turn to creating fiction if they have personal religious experience. More narrowly, I would think that it would be uncommon for religious people of this sort to become television writers. What leads me to believe this is that I have encountered very few fictional depictions (television or otherwise) of the experience of living with religious fate that have felt to me that they were based on any actual experiences on the part of the author. The Sopranos is an outlier in this respect; Carmela's religious experiences feel founded in real life.
The Sopranos does benefit from its religion being the one sort of religion that Hollywood has experience depicting. Since we've talked about Mad Men, we can bring up the one point that bothers the sort of person who posts on this site to no end: Peggy's family, despite being repeatedly identified as Norwegian, is shown to be Catholic. You can come up with ways to explain this away if you want, but it's something that does need to be explained away, and it suggests that that was the only kind of organized religion that the writers had any sense of how to depict.
This is pedantic, but it's clearly stated in Mad Men that Peggy's father was Norwegian and her mother is Irish Catholic.
You do bring up an interesting point as to whether Hollywood disproportionately depicts Catholicism over other Christian sects. Though I think a lot can be explained from the fact that the coastal cities have a lot of Catholics.
As a Midwestern Protestant, I always find this hilarious. The number of movie characters in rural Indiana who have a priest or something similar is such a comical East Coast perspective.
