Coffee shop noise is irrelevant, office noise might be relevant. You automatically pay attention even if you don't want to.
For me, noise cancelling headphones are a necessity. Impossible to get anything done otherwise.
What finally made me buy a good set of headphones for work was a cow-orker that would regularly come to my office to talk to a colleague about some project. Nothing to do with my work, but the words he used made me involuntarily tune in to the conversation every 10 seconds, just because it sounded relevant.
It's basically just ambient noises from a coffee shop, and you can choose a couple of different "environments". I pop that on in my headphones, and layer on some instrumental music. I love it.
Right now I'm in a cafe that has 50+ people and thumping bass music, all sweet white noise. With a beat.
At the moment, a couple members of the R+D team are discussing a new database schema, and I'm wishing that another manager hadn't swooped in an taken the place we were planning to move to a week ago.
Only to her. Everyone else silently thanks you. Don't let assholes define the narrative by feeling like an asshole because you asked an asshole to quit being such an asshole.
This was 6 months ago and she hasn't spoken to me since. I sometimes say hello and goodbye but she just blanks me.
Assholes will always find a way to be an asshole no matter what you do.
So she's even more quiet than requested. Sounds like a win. :-)
At least you have a door.
That said, I solved the problem of talking cow-orkers by ordering a second pair of the same high-quality gaming headphones I use at home. I turn on some music (or pink noise), and I can no longer hear anyone.