I think we need to differentiate between minor characters and major characters (or flat characters and round characters, to use EM Forster’s terms).
Viewers/readers are more forgiving of stereotypes in flat characters because their function in the main story is limited (and besides, they are viewed from the standpoint of the protagonist usually). It’s relatively easy to create interesting characters by pairing the stereotypical quality with something unrelated. Ex. A Christian girl who is also a racecar driver, a devout Muslim who raises poodles, a vampire that likes to sing Karaoke.
That strategy doesn’t work well with round characters because it has a manipulative formulaic quality to it. When a character only has external qualities, it is easy to traffic in stereotypes.
Perhaps one could make the argument that in cinema we never “get inside the brain” of even major characters. How much do we really know about Annakin Skywalker or Frodo aside from onscreen behavior? Perhaps the answer lies in the fact the audience is allowed to view a number of their private experiences that no other character has the privilege of doing.