Many don't have an intercom - the headsets are all (presumably) wired up in parallel and you can get interference problems with a mixture of types.
That's a very good point. I'd expect that the headphones are passively in parallel on old spamcan intercoms, but with individual active buffering on modern intercoms like a unit a pilot shop might test something on.
Does the problem always occur with the same instructor, or with instructors wearing the same type of headset? If so, and if my last suggestion doesn't work, perhaps you could try to get your instructor to wear a different headset for a lesson?