I've got the most recent Affinity Designer desktop version, and this problem was happening with the last version as well on my Macbook Pro running OS Mojave. There are 3 problematic behaviors that are making it impossible for me to use Affinity.
1) When I try to select any font other than Arial, the selected font displays for a few seconds and then the font turns back to Arial. This happens whether I have the type highlighted and using the type tool, AND when the text box is selected using the arrow tool.
2) When I try to select a font other than Arial, the dropdown menu of fonts in the Character panel closes immediately, so it's impossible to scroll to select the font I need.
3) If I manage to select a font by typing in the font name in the Character panel, the font displays at first, but if I resize the text box, it reverts to Arial.
I have Adobe Fonts and many of them are active. But I cannot use them in Affinity due to the issues described above.