There is a huge chance that your readers are just poor in understanding the medium. This happens a lot with people who claim to be animation fans who then freak out that the quality must be bad because they do not understand smear frames. (For those who don't know, is to deliberately distort a subject to sell an action. To have one frame represent many frames is a great way to make said action snappy, more powerful, etc.)
A "cute" art style in itself does not have to destroy anyone's set drama. There are tones of works that depending on your culture, the stylistic form of your art, or even some elements of your style, can give the shorthand telling of "this is cute". But said cuteness can be anything from just to the subject itself (ex: this character is cute to help contrast how not cute the rest of the world is) to a shared theme for the entire setting (which also does not have to destroy the dramatic mood, as anyone who as seen/read works like Madoka or any CLAMP piece).
But there is also cultural conditioning happening. What allows one form to be cute and another not? My mum thinks Sonic (in all forms, not just the new film) is one of the most ugly, disgusting designs she has ever laid eyes on. Since I was raised in a similar setting, I really don't find him appealing either. However for a lot of people he looks cute, even perhaps cool.
If people can take the soap opera of noodle people like Code Geass seriously even with all the poorly designed fan service (no hate, I love the series), then there is a place for any style for any mood.