I think you have three possible choices here:
1. Explain, and then draw really clear boundaries to prevent them undermining what you're doing.
2. Bring them onside through education and discussion (may be preceded by some time spent in option 1)
3. Don't tell them.
With most of our friends and extended family, when asked about our homeschooling, or when there were clearly mistaken assumptions about it that would be awkward not to address, we took the first approach. We explained that for the time being
we had gone off-piste, using a child-led approach and dispensing with much of the structure typical of traditional schooling. We said we were doing it because "at this point the kids are happy and thriving and learning like crazy." We said that we had done a lot of research, and addressed many of the obvious objections to our current satisfaction, and we hoped that we would be supported, or at least not undermined, as we continued moving forward on this path.
Then when the inevitable objections or concerns were voiced, we'd just parrot back "I appreciate your concern, but we've done our research and are happy with our choice for now." Or "I know you're just asking out of concern, but I've explained that for now we're not handling their education that way, and I need you to respect our choice."
All the "for now" and "at this point" phrasing helped, I think, because it reassured people that we weren't blindly committing to something forever, regardless of the outcome. If, contrary to our expectations (and more in keeping with their expectations, lol!), unschooling turned out to be a disaster for our kids, we'd be willing to re-evaluate.
We honestly didn't ever have trouble with people pop-quizzing our kids, but for older kids advocating for themselves one comeback that might work in some situations is "If you really don't know I can help you look that up."
When it comes to option 2, that's an approach we took with a couple of our closest friends and with my parents. I think there's a certain amount of understanding of the philosophy of unschooling that is best built through reading and pondering in the abstract. To what extent are humans natural learners? What is the nature of motivation? Is the traditional model of top-down learning of a body of information and skills still as valid in the 21st century? Are most things best learned in a specific sequence? Should learners be the primary agents of their own learning? All that sort of stuff. So for the people that you really hope to get on your side as supporters, you could give them some reading assignments (
might be a good book).
And then, once they have an understanding of the philosophical framework, they may need some help understanding how it works in real life. I've found that sharing a lot of cherry-picked experiences and observations on a family blog has been a good way of showing people how rich and robust unschooling can be in the day-to-day. You leave out the parts where your eldest is moaning about wanting potato crisps for breakfast and the middle two are squabbling over who gets first chance on the computer, but you mention the parts where your eight-year-old explains the Ancient Norse derivation of our words for the days of the week or where your family is harvesting sunflower sprouts from your kitchen sprouting jar project. And you take photos of your youngest with the huge pile of Dr. Seuss books, your of eldest poring over a page of historical costumes and of your family hunting for a geocache at some historical monument.
Another tactic that can help them understand what natural learning actually looks like is to ask them about something they were passionate about learning independently as a child, or about something they got interested in learning as an adult outside of the bounds of structured education. "Think about how you learned to build webpages. You didn't have to be forced. You didn't have to take a course." Or "Remember all the amazing pottery you did as a teen? How did you learn that? No one forced you. You did a workshop, and then you read up on wheels and kilns, and then you signed up for time at the co-op studio, and you found a mentor, and you pored over those supply catalogues, and went to museums and remember trying to fix that wheel? and ... "
As for option 3, that's where we went with my MIL. She is a religiously and temperamentally conservative former schoolteacher in her 80's and we knew there was no way we were ever going to get her on-side. We also knew that she would carry a lot of stress with her even if we managed to draw boundaries. Because she lives on the other side of the country and doesn't see us in person very much, we just allowed her to continue assuming that our homeschooling was very traditionally structured. When she came to visit us for a week here or there, we said we had decided that while she was there we would make spending relaxed time with her a priority. When she left she would always say how thankful and touched she was that we had rearranged our homeschooling to clear our schedule during her visit. Haha, you're welcome, mom!