TV shows are sometimes criticized for lack of realism due to most of the cast being too good looking. What is a show that has mostly normal looking people?

Most British shows, so Peep Show, Fleabag, etc. There's even Episodes, which makes fun of this all in a very meta story about a British show being adapted to American audiences and requiring only hot people for the new version.

Agreed on the UK shows. The IT Crowd, Black Books, etc
Peep Show wouldn't work if Jez and Mark were sorta, well-together.
Yes, Minister is populated by an awful lot of people that are quite average in appearance.
- Sir Humphrey is a stone cold smokeshow , with the brains to match.
  
  And don't even get me started on Sir Arnold.
European shows in general. Nordic Netflix shows usually have more realistic looks than US ones, even if they are a bit less "gross/unkempt" than some british ones.

Trailer Park Boys

TV shows in the US are criticized for that.

You can do a fun experiment to notice this plainly. Watch the first season of Broadchurch (brilliant British series). Every person is a believable, next-door looking person. Even the proverbial beautiful woman of the town is played by Jodie Whittaker, who is beautiful but not stereotypically so. The main character is David Tennant, who is attractive but quirky looking, and his partner is Olivia Colman, talented and normal looking. She's perfect to play a cop who aspires to advance in her career but hasn't been able to. And her character is magistrally played.

Now watch the only season of the USian remake, Gracepoint.

Tennant is the only actor returning in that version. His partner is Anna Gunn, for crying out loud. She's stereotypically gorgeous, she looks more like a former model that like a career cop. The "proverbial beautiful woman of the town" looks like a porcelain doll. (And her husband is from a token minority, another posturing you won't see so clumsily done in a British series. They are more naturally varied in casting.) After seeing Broadchurch, all the cast of Gracepoint look like molded plastic.

Shameless is a great example of this. I found the US version completely unwatchable-- not just because of the casting, but also the wardrobes.

[off topic]

I hate when they do a biopic and cast an actor who is much better looking than the actual person.

Tonya Harding was plain at best and certainly nowhere near as gorgeous as Margot Robbie

I remember when the Aileen Wuornos movie came out, my first thought was, "The kindest thing ever done for this woman was having her be portrayed by Peyton List."
- Leona Helmsley has entered the chat.
  
  The real one.
  
  https://www.advocate.com/news/2007/08/21/hotelier-leona-helmsley-dubbed-queen-mean-dies-87
  
  The woman they got to play her.
  
  https://www.wallofcelebrities.com/celebrity/suzanne-pleshette/pictures/suzanne-pleshette_326300.html
Tonya Hardin wasn’t unattractive. She wss fairly good looking.
- Nowhere near being in Margot's class.

Kevin Can F*** Himself has a bunch of actors that I’d never seen before and are very non-Hollywood pretty.

You're allowed to say fuck on the internet

If you don't like saying fuck, then don't fucking say it
- That’s literally the name of the show. I was the one who posted this:
- Might be fine for the internet, but not for the name of a TV show, even one that's on cable.