When you want to distance yourself from something or someone, there are several synonyms for the phrase "have nothing to do with." You could say "have no involvement with," "stay clear of," or "keep away from." Another option is "steer clear of," which implies that there may be danger or trouble associated with the thing or person in question. Similarly, you could say "avoid like the plague," which adds a sense of urgency to the situation. If you want to be more formal, you could use "eschew," "abstain from," or "renounce." No matter which synonym you choose, the message is clear: you want to avoid any connection to the thing or person in question.