All of them should/will work in your Mac Pro 2010. Apple has officially published a list of which video cards ought to support Mojave, and the Sapphire Radeon Pulse RX 580 8GB is on that list, along with the Vega 56 and 64. I don't have any reason to doubt that.
you might also want to check xlr8yourmac.com for other Mac users' experiences with similar/different graphics cards, which ones work right out of the box, and which ones need help. Technically speaking you can put a PC graphics card into a Mac Pro and it ought to work. Depending, of course, on a few things: Does the OS have basic support/drivers for it? are the specs of the card close to standard ? eg, no "tricked out" cards. and can you live without the boot screen, in case of troubleshooting, and the power cable must, of course, be plugged into the logic board.
I couldn't see or find any Mac drivers on the sapphire website, so I have assume that basic support is built into the OS. you'd have to check with xlr8yourmac.com for more clarification. The last graphics card I know about that worked in a Mac pro from 2008 or later was the Sapphire Radeon HD 7950 Mac Version, and even that one is way outdated. Of course, support for it (or any graphics card) will be better the newer the Mac OS you have.
good luck
john b