I work well with ambient noises (including music) as long as they stay ambient and don't command my attention - people talking too close by or putting on their music and changing it every half-minute or my flatmates clonking about with pots in the kitchen, that kind of stuff just drives me mad. Strangely, restaurant ambience and suchlike don't unless the conversation at the next table is too loud. Anyway, I always have music running to drown that stuff out and even when there isn't noise, to make some. I call it "giving the part of my brain that gets distracted easily something to play with so the grown-up part can work".
I'm pretty peculiar about the music I need for that. It can have vocals but not in my native tongue German. English is fine because despite being fluent in it I can ignore it well enough. Or choose not to. Sometimes, I'll take a minute and sing along to a favorite line before diving back in. It shouldn't be too simple because then that part of my brain won't stay engaged and will come bothering me again, but it shouldn't be too engaging either and demand active listening. Also, no playlists or (shudder) radio. I need albums. I do like vinyl albums because they make me get up and move a little every twenty minutes. I like music that has layers to it, rich harmonies or a strong beat, preferably both, don't much care if the depth comes from a horn section, an orchestra or heavy guitars. I've also experimented with playing two ambient albums at the same time and stuff like that to make it more textured. Then again, sometimes I'll just launch a drum machine on a semi-random pattern and be done with it. Within those parameters, it can be just about anything, no connection to what I'm writing needed and no particular style either. My mood is more of a factor than my project or any notion of process.