The mustard is a carrier so to speak for the rub. It holds the rub on the meat and imparts no flavor once the meat is cooked to temp. I use EVOO on poultry to deliberately carry less rub for a more delicate meat.
I use Olive oil, or nothing at all. The rub stays on even with no oil. Without oil, you can't get a heaping amount on, but that's fine with me. I eat it for the Pork, not the rub. If you use oil it helps break down some of the spices, where Mustard doesn't do that.
I'm a confirmed mustard slatherer. It's not as much an issue with butts because of the volume of meat vs bark, but on ribs, you need to cut way back on the salt in your rub. The mustard flavor cooks away but the salt in the mustard does not.
I like mustard cause you can puts tons of rub on those huge butts and it makes a super thick bark perfect for how i like pulled pork. I have yet to try EVOO, but i imagine that would work decent, too. I think without either you just wouldn't get the rub sticking as well nor that awesome flavor bark!