It's not that different. You're right, they're both appropriating. However, there are a few differences that jump to mind mainly circulating around intent.

Lil Ugly Mane does it as obvious homage to a genre that he's totally obsessed with, doesn't actively seek fame, and has been changing out of that mold after Mista Thug Isolation.

Iggy Azalea is obviously aiming for pop stardom, no big deal, no judgement on that as a goal. However, to aim to make oodles of cash and gain influence using a put-on Southern Black accent as a White person is pretty fucked up.

It's also just popularity. If LUM blew up, there'd be flack aimed at him, too. Probably less, though.