The term "un-objectionably" refers to something that cannot be objected to or that does not elicit any objection or criticism. Its antonyms would be words that convey the opposite meaning, such as "offensively," "disagreeably," "offensively," "controversially," or "inappropriately." These terms describe actions, words, or behaviors that are likely to arouse disapproval or provoke criticism from others. For instance, if someone behaves offensively, they are likely to upset others and elicit criticism. Similarly, if a statement is controversial, it is likely to spark debate and differing viewpoints. Thus, these words represent the polar opposite of "un-objectionably," which denotes something that is universally accepted and cannot be objected to.