one sided conversations

I know a couple of people who have mental illness. They ignore questions and just say something totally unrelated in response to a question.

Like I may ask how was your date? And they answer with "I'm trying this new diet and exercise regime etc...." And never answer the question.

Then I ask another question it doesn't get answered, they just go on about something else.

What is this?

It's called changing the subject. It's not something unique to people with a mental illness.

People do it when they don't want to discuss the thing you are asking about. People do it when they're not comfortable answering such personal questions. It's another way of saying "mind your own business".

I agree with lilyfairy. ‘Avoidance’ might be the term you’re looking for? They might feel they’re being interrogated.

I don't think that's what they are doing. I am not aggressive or rude, just asking normal daily questions, like "how did you date go" and they talk about something else instead.

It sounds like you know the situation better than us then. Have you tried asking the person why they aren’t answering your question about their date? Or do they just go off on another tangent?