I think I found the problem. For some reason the Affinity Designer font cache has some fonts included multiple times.
The export problem just shows up when I use fonts that are multiple times in the font cache, e.g. Asap Regular or Montserrat Bold. For all others it works fine. I checked in my C/Windows/Fonts/Asap which font weights are installed and how many times. There were multiple times the regular weight, so I uninstalled the duplicates. But in C/Windows/Fonts/Montserrat are no duplicates of the Montserrat Bold that I could uninstall. Unfortunately, I sometimes have to rewrite my Windows fonts. It seems to me that a problem occurs when I reinstall the fonts.
Regarding your question: I attached the screenshot with the export settings. My PDF viewer is Adobe Reader XI (Version 11.0.23). The same problem occurs when I use PDF X-Change Editor (Version 6.0 - Build 322.7).