This study investigates how online counterspeech, defined as direct responses to harmful online content with the intention of dissuading the perpetrator from further engaging in such behavior, is influenced by the match between a target of the hate speech and a counterspeech writer's identity. Using a sample of 458 English-speaking adults who responded to online hate speech posts covering race, gender, religion, sexual orientation, and disability status, our research reveals that the match between a hate post's topic and a counter-speaker's identity (topic-identity match, or TIM) shapes perceptions of hatefulness and experiences with counterspeech writing. Specifically, TIM significantly increases the perceived hatefulness of posts related to race and sexual orientation. TIM generally boosts counter-speakers' satisfaction and perceived effectiveness of their responses, and reduces the difficulty of crafting them, with an exception of gender-focused hate speech. In addition, counterspeech that displayed more empathy, was longer, had a more positive tone, and was associated with higher ratings of effectiveness and perceptions of hatefulness. Prior experience with, and openness to AI writing assistance tools like ChatGPT, correlate negatively with perceived difficulty in writing online counterspeech. Overall, this study contributes insights into linguistic and identity-related factors shaping counterspeech on social media. The findings inform the development of supportive technologies and moderation strategies for promoting effective responses to online hate.