Example: I'm in the middle of saying פסוקי דזמרה and one of my dad's friends comes up to me and says "hello...". Do I have to ignore him or may I respond "hi".
Shulchan Aruch (OC 51:5) when discussing the laws of Pesukei Dezimra, says as follows:
בין המזמורים האלו שואל מפני הכבוד ומשיב שלום לכל אדם ובאמצע המזמור שואל מפני הירא' ומשיב מפני הכבוד:
In between these psalms one may ask [of another's welfare] out of respect [for that person] and may reply greetings to any person. And in the middle of the psalm he may ask [of another's welfare] out of fear and he may reply out of respect.
In short, even if it's not going to ruin your concentration by not replying, you are still allowed to do so in between paragraphs.
Nevertheless, the Mishna Berura in 66:2 says that if the person will not be upset that you didn't answer him, you may not answer the greeting.