It's interesting how some of these kinds of protective clothes are seeping into non-working class/craftsman jobs, as a way of honoring/co-opting craftman heritage.
Warby Parker
Warby Parker retail workers wear special blue shirts/dresses/smocks, perhaps because opticians traditionally wore short lab coats and were essentially lab techs. I like that there's a variety of options depending on gender, like some kind of start-up culture Star Trek.
Ippudo X Engineered Garments
For their NYC shops, ramen shop Ippudo worked with EG to develop special aprons for their kitchen managers. I'm not sure if they really wear these day-in, day out, but again I enjoy the romanticism that this clearly invokes. You like to think that these people who prepare your food are clinically disciplined. I also like that there's several pieces to this: apron and jacket, making the whole thing a bit modular and oh so much more versatile. MODULARITY OH GOD YES.
Margiela
Perhaps the most obvious example of what I'm talking about in fashion. Margiela workers both in-store and otherwise done white lab coats, I've heard, to maintain the continuity between what they do and the craftsmanship that is their core. I've personally been trying to get a lab coat from them for years but they don't sell them to civilians.
I always get a kick out of the fact that the store workers seem to really hate wearing them. Seriously, I don't think I've ever seen a Margiela associate smile, but that could just be the nature of fashion/retail work. They also treat these coats like garbage, spilling coffee and pen ink all over them.
Look at this unhappy camper.
Will Leather Goods black deerskin apron (morbid love here). I'd like to see how to actually wear this well. The logo hurts it, I think.
Will Leather Goods waxed canvas(?). Pretty easy for the worker-look... even if it's very cosplay.
Paul Harnden Apron dress. Obviously more conceptual, but it's an interesting look. It's got a bit of the "home" look, but that's also because it's a more delicate fabric. Had it been in canvas it'd look like a weird peasant worker outfit(?)
Carol Christian Poell's infamous vest-bag, but some rarer looking model. The back gives it the more apron-y look. Even from the front it doesn't give off completely vest-like vibes. 
Carpe Diem & related lines seem to enjoy a take on lab coats, in fact this coat cut is referred to as the "lab coat"
bonus Bray Wyatt. Not his best outfit, but best I could find with his apron. He's supposed to be a bayou cult leader.
