Doesn't the question of whether this sentence would be "too harsh or rude or unprofessional" depend largely on your relationship with the other person? What is appropriately harsh in an email to a subordinate who has already been warned about his or her poor performance might be completely out of bounds if you're addressing a colleague of equal rank – let alone a client or your boss. Since you've only identified the target of this sentence as "a person," it's very hard to answer your question as asked.
As for how one might translate the sentence, I'd say this is one of those cases where it's difficult to come up with something that is both close to the meaning of the original and also idiomatic in English. 誠実 is particularly problematic, because it involves not just "seriousness," but also sincerity and even honesty. In this case, at least, I think something along the lines of "Can you please conduct yourself with a bit more integrity?" might be more in the spirit of the original than your "Can you be more serious with your work?"