If you need some synonyms for the phrase "refuse to accept" in your writing, there are plenty of options to choose from. You might say that someone "rejects" or "denies" something, or that they "turn down" an offer or proposal. Someone could "dispute" or "contest" a claim, or "oppose" or "resist" an idea or decision. They could "object" or "disagree" with a course of action, or simply "refuse" or "decline" to participate. Whatever word you choose, make sure it conveys the right tone and emphasis for your intended meaning.