And if they want a precise definition of "disturb", you can get into the not-too-difficult math of superposition and entanglement.
I'm a math grad student and I consider the math of entanglement and the like to be not easy. There are two types of consciousness-causes-collapse proponents. The first type who doesn't know much physics will find entanglement to be pretty difficult (they need to already understand complex numbers and basic linear algebra to get the structure of what is going on). Even a genuinely curious individual will likely have trouble following that unless they are a mathematically inclined individual. The second, much smaller group of people, are people who already understand entanglement but still buy into consciousness-causes collapse.They seem to have developed very complicated and sometimes subtle notions of what it means for things to be conscious or to have intent (almost akin to theologians). So in either case this avenue of attack seems unlikely to be successful.
If one is more concerned with convincing bystanders (as is often more relevant on the internet. People might not change their minds often. But people reading might), then this could actually do a good job when encountering the first category by making it clear that one knows a lot more about the subject than they do. This seems to empirically work in real life also as one can see in various discussions. See for example the cases Deepak Chopra has try to invoke a connection between QM and consciousness and he gets shot down pretty bluntly when there's anyone with a bit of math or physics background.
You're right; maybe I'm overestimating my ability to explain things so that laypeople will understand. But there are some concessions you can make to get the idea across without the full background of complex linear algebra - often I use polarizers as an example, because most people have some experience with them (from sunglasses or 3D movies), and from there it's only a hop, skip, and a jump to entangled photons.
I do try to explain so that people feel like the explanation is totally natural, but then I often run into the problem of people trying to reason about quantum mechanics "in English", so to speak, instead of going to the underlying math to learn more. Any suggestions?
If it's worth saying, but not worth its own post (even in Discussion), then it goes here.
If continuing the discussion becomes impractical, that means you win at open threads; a celebratory top-level post on the topic is traditional.