From what I gather, Oriental is usually acceptable when you're talking about fabrics, markets, medicines, or the classical notion of Orientalism through the fascination/exoticism of the art and culture from the Middle East and Asia from the 19th century.
When you refer to Asian people as Oriental, that's where you hit the problem. It's not comparable to a hard-hitting slur, but it comes off similarly to Urban. People say Urban Contemporary music or Urban Fiction, but it rubs people the wrong way when Black people themselves are called Urban.