Would it be ok to use red cabbage for this recipe?

You could, but I wouldn't.

From a flavor perspective, there's no issue.

From an aesthetic standpoint, using red cabbage will result in something much different than the photograph. All the vegetables will be bright pink.

It's your call if you want that type of presentation.

Personally, I would find it odd, but that's just me...

Yep. It's just a little more robust than white cabbage, and it will dye your broth and veggies a blueish colour, but if you're fine with that then you can totally use it. (If you put some acid in it while cooking, it'll turn out pink-purple instead of dark blue)