I’ve been firmly taught to wear them. And firmly taught not to wear them.
I’ve lost audio through not wearing them, and I’ve lost human connection through wearing them.
Here’s my rule: You can happily get away without wearing headphones, if you are using two omni mics, one in each hand, you practice, and you have your phone switched off. That’s a nice documentary technique to boot.
Earbuds? Really this is just to let you know you’re still recording (the disc isn’t full or battery flat), and that there isn’t some loud interference from a buzzing mobile phone or the like. So fine for news where the interviewee is plum in front of you, and there are other journalists around. At times like these, try to use a recorder with XLR sockets rather than mimi-jack, as it’ll be less susceptible to that phone buzz. And it would be foolish to not have a flag on the mic or a printed windscreen when there are cameras, influential people, and your journalistic counterparts around.