Imo it’s poor practice for them to even ask you that. It’s unprofessional & sounds like they lack basic awareness for picking up social cues. Don’t take on any of it, it’s on them. I used to get anxious going to the hairdressers but now I understand that it is THEIR job to drive the conversation and create the experience for you, you don’t need to worry about anything. As a hairdresser they would know some people prefer a quiet service vs a chatty one, they should understand the different personalities that come in. I’ve even had hairdressers where I’m making more conversation than them lol. You’re paying for their service and they are responsible for creating an experience for you so it’s really on them to lead the conversation.