When it comes to how you dress on TV, the main thing is you don't want to confuse people and you want to send a consistent message. So if you are a surgeon, being in scrubs is going to be more appropriate for doing a TV interview than if you're always in scrubs but then you get dressed up in a suit and tie for your TV interview. Now you can always ask the TV reporters and producers what they prefer if it's a really big deal and you have the time to make a choice but in general, anything that you wear that signifies your medical profession exactly what you do, the better. There's nothing wrong in fact, it's a good thing to have the white doctor's jacket on. Although if you have a choice between pure white and off white, go with the off white, it's less glary on TV, and it won't wash you out as much it'll be easier to see your face if it's a slight off white but if you always wear a pure white doctor or medical coat, then continue to do so for interviews.
You don't have to have the stethoscope around your neck if you never use that. But if you do, don't take it off before the interview, keep it there. It's another way of sending a message to the public that you're the expert. This is what you do. you're practicing professional. You're not just a generic talking head weighing in on all subjects of the day.
So always think about what it is you're wearing, and how it can send the message of your expertise.