How to ask a knowledge question without causing offence?

Solution 1:

I would ask the question in this way: "How familiar are you with X?".

Asking "Are you familiar with X?" suggests that the answer is either yes or no, while my question is "accepting" to all levels of understanding.

Solution 2:

Be forthright. Ask them how much they know. Only the most sensitive will be offended, and anyone with sense will understand the need to know.

Coming at the subject obliquely is more likely to offend since your ambiguity will be construed as confirming their fears.