>OpenShift runs whichever container you want with a random UUID, so unless the Docker image is prepared to work as a non-root user, it probably won't work due to permissions issues.
It’s not quite random. Every namespace gets assigned a unique block of 10k UIDs and the default container UID is the first in the block for all unprivileged users. Granting access to a higher powered PSP (actually a security context constraint which was the basis for PSP) changes the defaulting.