I'm talking about when the viewer completely ignores the message that the publisher is trying to communicate with the cover. The exact opposite of what you're talking about. I'm talking about when they don't buy into the cover's message because the characters were hand-drawn Asians instead of photographed Americans (or whatever else).
How is the particular art style chosen for the cover not part of "the cover's message"?
You say people are ignoring the supposedly "obvious" message of the cover, because of how the characters are drawn. But "how the characters are drawn" is part of the message, even if it might convey different things to different people who come at it from different experiences.
What I mean is, take the exact example you gave: "three teenagers stand in battle-ready poses in the foreground, while the background includes a battleship and a looming, angry face". But you can't just reduce the "message" to the mere physical elements the way you're doing here.
That exact scene you describe could be drawn using the art syle of Avatar the Last Airbender. Or it could be drawn in the style of the Justice League Unlimited cartoon. Or it could also be drawn in the art style of The Powerpuff Girls. Or it could be drawn in the art style of Rick and Morty. Or (and this was the intended point of the example) it could be drawn in the stereotypical-romance-cover-art-style of the image I linked above.
That choice--even keeping the same basic components of the scene the same--will create VASTLY different impressions in the audience of what the people who see it think the intended "message" of the image is. And those different impressions will be informed, in part, by their prior experience with other media that use a similar art style as well. Cultural context is an intrinsic part of that kind of non-verbal communication, and it absolutely influences the "meaning" that people read into a work or an image.
(For example, doing your example heroes-in-front-of-a-battleship scene in a cutesy style will convey one sort of meaning to a person who grew up watching Powerpuff Girls... but it might not have even remotely the same connotations to someone who grew up watching Happy Tree Friends instead.)
In short, I maintain that choice of art style can (and should) convey meaning. But, since that meaning is imprecise and context-sensitive, I think it's worth giving people the benefit of the doubt in situations like this.
If someone's only experience of that art style is it being used in a certain specific genre, their perspective could be as skewed as the guy who was raised on Happy Tree Friends would be as far as what the choice to use that art style "really" conveys. It doesn't necessarily mean they're racist, or being willfully ignorant. They might just be operating from a smaller reference pool than I am, and thus reading a bit more specificity into the meaning of the art style choice than actually exists. It's not like there's a hard and fast rule to this kind of interpretation, no matter how "obvious" it might seem to fans of the work who are more experienced in these waters.
Anyway, in a situation like this, I prefer giving them the benefit of the doubt, rather than condemning them in absentia.