Handling disagreements in online conversations requires patience, empathy, and effective communication skills. Start by staying calm and composed, and avoid resorting to personal attacks or insults. Focus on addressing the underlying issues or concerns respectfully, and listen actively to the other person's perspective. Be open to considering different viewpoints and finding common ground, even if you don't agree on everything. Finally, agree to disagree if necessary, and strive to maintain civility and respect in the conversation.