As soon as someone finds chat distracting, they can either block the person or switch to Focus mode. Resigning seems like overkill to me. They could also ask the other person to just stop - if they did and the streamer persisted, that's when it becomes inappropriate, but until that point I don't see anything wrong with it.
Etiquette check on Youtubers and Chess.com
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I use several different sources to study chess. YouTube is often one. I am noticing a trend in a lot of the popular chess YouTube channels where the YouTubers start a game, and then a few moves in they start sending chat messages asking the person, "Do you ever watch <insert YouTuber's channel> here?" or, "Whose videos do you watch the most when learning chess?"
In most older videos, the other players simply don't respond. What I am seeing more often now, especially during the Twitch streams, is there are more and more people resigning the game after it starts because they aren't interested in helping to sell someone's brand. Keep in mind, this is typically within 2-3 moves that the YouTubers start asking questions about their channel (in one video the other player literally resigned 5 seconds after the YouTuber started asking questions.
I joined Chess.com to play Chess. When I join a game on Chess.com, it is to play chess. I am not here to help some YouTuber sell their brand--and a lot of folks that ignore the chat messages don't realize their gameplay is putting money in their opponents pocket via monetization and Patreon.
I'll leave it as an open question to see what people think.
Is it poor etiquette in a game to start messaging the other player in order for a YouTuber to try and use the game to sell their brand?
IMO, I think it is inappropriate and unsportsmanlike behavior.