We are using Oracle DB (19c) running on Oracle Linux 7. Both have patches that need to be applied and the DBA's do not want to do both at the same time. The question keeps coming up about which we should do first. Patch Oracle Linux 7 then Oracle Database or the other way around?
My feeling is that Oracle does enough testing that we could do both at the same time, but if we had to do them separately then the OS should be done first. We also have dev, qa, data guard, disaster recovery, and production. So there are enough servers where any issue that comes up we'll see it before we get to production.