There's a mystery to what it is that makes certain works of art, books in this case, move one's heart most. It's something other than innate quality. I'm intermittently in this community because I especially love Tolkien. I've read "Lord of the Rings" dozens of times. But actually the "Silmarillion" is my favorite book and "Leaf by Niggle" my favorite story. I don't think that's the common attitude. Anyway, I'm getting around to that "That Hideous Strength" is one of my favorite books ever. I'm not comfortable recommending it, though. I know more people who liked "Out of the Silent Planet" and "Perelandra" and didn't like "That Hideous Strength." A lot of people.
All three have a religious subtext. "Perelandra" more than "Out of the Silent Planet" and "That Hideous Strength" most of all. In all, Lewis is capable of depicting extraordinary beauty, completely alien in the first two and more earthly and quite distinctly English in the last. It's true that "That Hideous Strength" is often very dark. Lewis is capable more than anyone I can think of of depicting real Evil. There are characters in it that make my skin crawl.
Tolkien didn't like Lewis' depictions of evil. He didn't disagree with them: he felt that it was a wrong thing to concentrate on, that such things should be turned away from. He was particularly upset that Lewis dedicated "The Screwtape Letters" to him (Tolkien). "The Screwtape Letters" are a series of letters written by one devil to his devil nephew. It's not obscene or anything, but after I finished reading it, I felt sort of dirty. Lewis really does do Evil well.
So "That Hideous Strength" has that same repellant depiction of evil and is arguably sexist and anglo-centric. But it contains a vision of, for me, wonderful goodness and joy. It is, as I say, one of my favorite books. My experience with others leads me to think that it probably won't be one of yours.