“Guten Tag!” is German for “Good day!” A food pun is “Gluten tag,” a game of tag involving bread (gluten). “When German children play a game involving touching each other with bread…it’s called gluten tag” was posted on Reddit—Jokes on December 22, 2015. “What do you call a game where Germans throw bread at each other? Gluten tag” was posted on Reddit—Jokes on August 14, 2018.
   
“How do German breads greet each other?/“By saying ‘Gluten Tag!‘“ is a related joke.
       
         
Wiktionary: guten Tag
Etymology
In accusative case, because it is short for ich wünsche einen guten Tag! “I wish [you] a good day!”.
Interjection
guten Tag
1. good day, good afternoon
2. hello
     
Wikipedia: Gluten
Gluten (from Latin gluten, “glue”) is a composite of storage proteins termed prolamins and glutelins and stored together with starch in the endosperm (which nourishes the embryonic plant during germination) of various cereal (grass) grains. It is found in wheat, barley, rye, oat, related species and hybrids (such as spelt, khorasan, emmer, einkorn, triticale, kamut, etc.) and products of these (such as malt). Glutens, and most especially the Triticeae glutens, are appreciated for their viscoelastic properties. It gives elasticity to dough, helping it rise and keep its shape and often gives the final product a chewy texture.
     
Google Groups: alt.humor.puns
Thanksgiving And Election Puns
Greg Evans
11/30/00
(...)
> > Sounds like a guten Tag.  KM
>
> Is that like playing laser Tag?
 
I prefer gluten Tag—an altogether more ful-filling game for well-bread people.
 
Reddit—Jokes
When German children play a game involving touching each other with bread…
submitted December 22, 2015 by nwolf51
it’s called gluten tag.
I’ll show myself out.
     
Google Groups: EWB-NEU Uganda Team
Meeting 2/15
Uganda Program Director EWB-NEU
2/15/16
(...)
Bad Joke of the Week:
 
Have you heard about the game German children play where they chase each other with pieces of bread?
It’s called gluten-tag!
 
Reddit—Jokes
What do you call a game where Germans throw bread at each other
submitted August 14, 2018 by SodiumWeasel13
Gluten tag
COMMENTS
wartooth6
Jokes about German food are the wurst.
     
Reddit—3amjokes
What do you call a game where Germans throw bread at each other self.3amjokes
Submitted August 14, 2018 by SodiumWeasel13
Gluten tag
 
Twitter
3AM
@3AM_Jokes
What do you call a game where Germans throw bread at each other… Gluten tag
11:27 PM - 13 Aug 2018 (Posted after the above.—ed.)
   
Twitter
Jokes OK Please
@jokesokplease
What do you call a game where Germans throw bread at each other. Gluten tag #joke
2:10 AM - 14 Aug 2018
 
LaffGaff
By laffgaff August 16, 2018
Bread Throwing Joke
What do you call a game where Germans throw bread at each other?
Gluten tag.