R9 380 is not an RX card. They SHOULD be able to work in most rigs co-mingled but you're combining two different chip architectures, and drivers may be a problem in that case. Basically, drivers old enough to be stable on the R9 may not work well with the RX and vice versa.
There's no fundamental reason you couldn't mix the two, but the only way to find out for sure is to try and see what the results are, if you have problems, drivers would be the first place to look for a cause.
They are both GCN - it's not nearly as much of an issue as trying to mix GCN and TerraScale cards on one machine.
Officially, ALL of the driver versions that support the RX 5xx series still support *ALL* GCN cards - back to the HD 7750/7850/7870/7870XT/7950/7970/7990 much less the R9 3xx series.
With that said, however, I'm not convinced AMD actually TESTS their newer driver version on the HD series at all and am iffy that they test them on the R9 2xx series - the R9 3xx series is recent enough they SHOULD still be testing in those though, and most of the 3xx series used identical GPU chips to the R9 2xx series and a lot of the GPUs in the R9 3xx series date back to the HD 7xxx"GCN" series cards.
Nvidia is another story - different manufacturer, different drivers entirely, you CAN mix AMD and NVidia but it's a major stability hit to do so, and on LINUX it's a very picky process to get them to work in the same system at all and has some serious limits on how you can do so.
