I have nvidia GTX950 on one host and ATI RX580 on a other.

I never received a GPU tasks !

ATI RX series cards should get WU with Catalyst 18.7 1 and that driver hasn't given me any issues on other projects (except maybe Einstein@home but only on multiple WU/GPU and not sure it's the driver's fault). Downgrade your driver should get the RX 580 working without hurting your other projects. If it does, please report back what project's WU had an issue.

My nVidia 1060 3GB and RX 550 are in the same computer under latest Windows 10 - 17738(?) with ForceWare 19.3.1 on the nVidia, Catalyst 18.7.1 on RX 550. Enigma can run 12 WU (6 per GPU) at once limited by the 6 CPU cores (1060 wants 0.9 cores/WU).

Not sure why your nVidia isn't getting work.
Try a DDU driver cleanup and clean Forceware install?