To behave or react indifferently is to show no interest, enthusiasm, or concern. If your friends wish you "Happy Birthday!" and you shrug your shoulders and walk away, you're responding indifferently, showing that you're really not interested in celebrating.
Responding indifferently suggests a detached or unconcerned attitude, indicating a lack of emotional investment. While it might imply a cold or uncaring reaction towards the concerns or suffering of others, it can also indicate impartiality or lack of bias. A person who responds indifferently to public opinion isn't necessarily being rude; they may have simply decided that other people's opinions should not necessarily influence their own actions or choices. In that case, responding indifferently is being emotionally neutral or unaffected.