I don't think I've danced with someone who was actually chewing gum at the same time (and I don't want to)
In my first couple of years of tango lessons, there were breaks during which we were given information on the historical, social, and practical aspects of tango to go with the movement theory: Dispelling the myths about tango in bordellos, comparing and contrasting the great orquestas, outlining the códigos then and now, talking about manners, discussing expectation vs. reality regarding how long it takes to learn tango and be accepted into the community, even recommending brands of shoes. In those moments, personal hygiene and physical conduct were regular topics.
The teachers were insistent that while it's crucial that your breath smell good, chewing gum is gauche and Not Done. They were unanimous that the best option was to keep a travel bottle of mouthwash in your dance bag, and to take that with you and use it each time you visit the restroom. Honorable mention went to mints tiny enough to crunch in the mouth during a cortina. Gum?
Never.
The person who ran the milonga where I worked had an ongoing, close-to-hot war with gum-chewers. This mostly had to do with the fact that they left gum stuck to things – a blacklist offense if caught. But she did regularly muse aloud, "Who chews gum while dancing?"
My friends who danced more swing and Latin at the time said that in those worlds, it was close to universal, so I imagine that's "who." While the studio where I worked was "all tango, all the time" when the owner was there, she rented the space to a kizomba school. As the barman and general factotum, I know that – not tango – is where the gum came from. Ick.