Well, I'm currently running two campaigns in the same setting during divergent time periods: One during the height of an Empire, and another in the long-term aftermath of that Empire's collapse.
For the later campaign (which is the "main" one), I prefer giving things a very grim Brom-like look. For the earlier campaign, though, I like giving things a more anime-style look, especially in regards to the Imperial Psi Brigades, Ceramic Spelljamming vessels, and other such elements.
In regards to products, I guess it depends on the setting. Anime tossed in with other various art styles wouldn't bother me, but if used as the primary "look" of a product, I'd certainly hope it compliments the style of the material. If I wasn't familiar with the product, I'd certainly be wondering what sources within the Anime genre the book was inspired/derived from.
And no, I don't like the art-look of 3E. I can't rip on it enough, so I'm not even going to start.