The adjective uppity is an informal, somewhat old-fashioned word. When used to mean "arrogant" or "presumptuous," it is no more offensive than either of these synonyms. In its meaning of "aspiring to a rank or position higher than one deserves or is entitled to" it is decidedly disparaging, the implication of the word being that the one described does not deserve or is not entitled to rise in standing. Beyond this denotation, however, uppity has a long history of being applied to members of racial minorities and especially to Black people. Its association with such uses, and the bigotry they represent, means that when it is used to describe a member of a racial minority it is likely to be considered especially offensive.
As someone with a job involving regular public speaking before some potentially-sensitive audiences, I’m always afraid that some word I use will turn out to have a hurtful impact on people despite being completely innocuous to my ear. Thanks for pointing out another one to add to my “don’t say this word anymore” list! Potentially saved me some awkward conversations.