Nonjudgmentally is a term used to express a person's impartiality and neutrality towards a certain situation or person. There are several synonyms that can be used to convey a similar meaning, such as objectively, neutrally, impartially, fairly, and objectively. If you want to emphasize the idea of being open-minded and unbiased, you may use words like unperturbedly, dispassionately, or equitably. Some other words that you can use to express this concept are tolerantly, leniently, and forgivingly. Ultimately, the word choice depends on the context, tone, and purpose of the text.