Question Best metal Graphics card for Mid 2009 Mac Pro. Main use: Adobe Premier.

Yes, that should work. Although you'll have some difficulties installing OS X. As the RX 580 won't have a boot screen. Since non-Apple video cards don't have the right EFI they won't function until the OS loads far enough to load the drivers. You'll want to keep your old GPU around for diagnostics.

I believe you also need to flash the Mac Pro firmware from your 4,1 to a 5,1 (2010 MP). This also lets you use faster CPU supported by the 2010 model.

MacRumors is probably the best place to get detailed help on how to get your legacy Mac Pro to boot into Mojave.

MODS: I'm unclear as to what forum policy is in getting real Macs to run unsupported versions of OS X. If it's the same rules as a hackintosh or wide open discussion since they are both Apple products.