Game won't allow me to play without glasses, but says they're restricted for the level Black Diamond

That is because you need glasses with the property hero.isPathClear() for this level.
The arrow is pointing at the mahogany glasses because they are the best glasses you have. I do agree that is misleading. Really the arrow should point at the cheapest glasses with the required property. Alas, it does not. What you need to do is buy glasses with the .isPathClear() property. The cheapest glasses with that ability are the “Hardened steel glasses”, available for purchase at 250 :gem:. Alternatively, you could splash out now and get the “Crude telephoto glasses” for 540 :gem:, which would be stretching your wallet a little, but would probably save you from upgrading your glasses again until later, at which point I suggest the Twilight glasses. At the moment, however, I think the “Hardened steel glasses” are your best bet.
I hope this clears up the confusion.