While I mostly agree with Joshua's view on this matter, I think the position is not entirely vacuous. While most people who use this particular false dichotomy are, as Joshua says, mostly lying to themselves about the benefits of ignorance, there are cases when knowing more does subtract from your ability to enjoy something.

But here's the thing: these things tend to be human created things rather than natural things. Examples:

1. I once saw a guy do a really impressive magic trick. I liked it so much that I bought the trick. The store guy took me into the back room and showed me how it worked. I immediately felt a sense of deflation, and regretted buying the damn thing.
2. Humor often works this way (Douglas Adams has often made this point): your ability to enjoy certain jokes may depend on your ignorance. You'll hear people roaring with genuine laughter and find yourself feeling not even a smidgen of amusement. Not because you don't get the joke, but because you do get the joke, but also know other things that make the joke seem remarkably stupid (often this is scientific knowledge, but not always; sometimes it is simply a more sophisticated sociological understanding of something for instance). I can't think of a good example off the top of my head, but I'll add one if I do.
3. Genre fiction becomes less enjoyable once you learn to recognize the commonplace tropes and narrative patterns. They become especially jarring if you can tell badly executed patterns from good ones. And even the best ones seem sort of hollow: technically perfect or even amazing, but somehow lacking in value and substance.

These things amount to a sort of Dunning–Kruger Effect analog for aesthetics. Just as the ignorant can enjoy a false confidence that is denied to the expert, the ignorant can also enjoy a false aesthetic that will seem hollow to the expert.

But as I said, this is nearly always only true of human created things. I have never felt this about anything natural. In my experience, people who prefer ignorance for things where science has richer explanations to offer are extremely tied up in their human identities and fail to appreciate things outside of projection of human desires and stories onto them. The skies are a perfect example. They are full of constellations representing the major Greek gods and demigods for example. For some people, the Greek mythology is preferable to a deeper understand of cosmology at a pop-science level.

For such people, looking up at Andromeda is a reason to think about the story of Perseus and Andromeda, the roles of Cassiopea and Pegasus, etc. etc. If that's really all you see or want to see when you look up at the sky, it's a sad little life (the Andromeda story has practically its entire star-cast up in the sky; pun intended).