No, saying "no need to apologize" is not considered rude. In fact, it is a polite and understanding way of responding to someone who has apologized for something they may feel responsible for, but that might not necessarily warrant an apology.
When you say "no need to apologize," you are essentially telling the person that you understand that mistakes happen or that there was no harm caused, and therefore, their apology is not necessary. It's a way of reassuring them and preventing them from feeling unnecessarily guilty or burdened by the situation.
This phrase is often used in situations where the person may be overly apologetic, has made a minor mistake, or when the situation was out of their control. By saying "no need to apologize," you are expressing empathy and letting them know that you hold no ill feelings towards them for what happened.
Of course, as with any communication, the tone and context in which this phrase is used can influence how it is perceived. If said with genuine kindness and understanding, it is unlikely to be seen as rude. However, if said dismissively or insincerely, it might come across as rude or insincere.
In general, responding to someone's apology with compassion and understanding is considered a thoughtful and considerate approach. It helps foster positive communication and reinforces a sense of empathy in the interaction.