that's weird. Could you please try removing Royal TSX from your /Applications folder (moving it to the trash), redownloading the latest release from here and installing it again?
I just waited for the next minor update to come out, and the issue is gone.
When I go to Properties on an RDP (or any?) object and try to change its icon, I get a frame where the icon changer should be. If I hover on the menu, I can even see icon names in a tooltip, but I can't see the icons themselves. The cursor changes to a typing-cursor over the search box.
I use Mojave dark mode with the latest public release of TSX v4.