Mojave beta installed, and the fonts look equally atrocious. They are blurry, indistinct...and just bad. One of the reasons I bought a 5K iMac (three of them, actually) was to have great fonts. I am beyond angry that I will now have to sell them.
Can you post some screenshots? I find hard to believe that fonts on a retina display can be blurry and indistinct, when the antialiasing text weight is almost the same.
Those screenshots were both in Waterfox. I also tried in Safari (didn't take any shots, though) and the fonts looked identically bad in that browser as well.
The normal UI's fonts are also worse -- about the same as the browser screenshots. Fonts are indistinct and blurry, and very light. All the result of greyscale aliasing only, I presume.
Either Apple disable "LCD font smoothing" for retina displays, or there is a bug somewhere. Because in Mojave on a non retina screen "LCD font smoothing" has got the same weight as before. And on your screen it clearly doesn't.
I hope it is a bug. If the weight were the same, it'd at least perhaps be tolerable on a Retina screen. I know the technical reasons, but I just don't understand why Apple can't leave it alone for desktop systems.