I agree. They're all trying to make sense of the Lord of Light but each person's view of "it" is different to a certain extent but everything is attributed to "it" which might contradict another person's faith. Melisandre acts like she knows all about her god and is the supreme authority on its religion, but then gets that information from Beric which goes against what she believes her god wants, does, can do, or is all about really. They're all trying to understand the Lord of Light but each in their own ways and trying to piece if all together is impossible. Melisandre might think she's the high authority on her religion, but she has just as many questions as everyone else and only knows what powers she's able to do and nothing else. Like you said, she's just throwing shit against the wall too! The powers are very much real as we've seen, but their religion around it is the mystery and differs from person to person. For all we know, it could be some old dude playing a role-playing board game based on Westeros.
It mirrors the old days of religion in our world and the oral traditions that carried on those religions but were warped over time due to each person's individual beliefs or wants making each person's version of their gods different than the others and the overall views of those gods get more and more distorted over time like a game of telephone. Much like any religion today even where many people might identify themselves as a follower of this or that religion, but they have their own individual interpretations of their holy books or what is right or wrong to them.