People singing when you're trying to have a conversation

I wonder if anyone else experiences this. I go on trips with my friends a lot which means we spend a lot of time in the car. Pretty much at all times we have the radio going, which is fine by me. I keep it low enough so it's like background music and everyone can still talk. But what really grinds my gears is when the person I'm talking to just starts singing along to the music, mid conversation.

I don't know why this bothers me so much. They seem to be paying attention, but it just feels so disrespectful? Like, we were both engaged in a good conversation, do you need to act bored?

What do you guys think? Is this something you'd be peeved at?