The above link is to a primary school held in very high regard in England and it is interesting that the FRONT page of their home page highlights " class debate- did the moon landing happen" with a picture of 9 & 10 year old children in school uniform debating the issue.
I don't think it's necessarily a stupid subject to discuss you could use it as an exercise in critical thinking. Students could be assigned to each side of the issue. Halfway through the exercise, the students would switch sides and argue those points. The teacher would have to be clear that the vast majority of people who are in the relevant fields do not support the hoax theory.
For example, one thing the conspiracy theorists think proves the landing is a hoax is the fact that some videos, the flag appears to be flapping. But this was because the flag had just been placed, the inertia from when it was let go caused it to move. Also, the astronauts accidentally bent the rod a few times causing the flag to move. The process of making an argument, then being challenged by the counter argument could be a good way to teach critical thinking.
The only problem I have with your OP and other things you have stated is that you assume the the hoax theory is equally as valid a point of view as not believing the landing is a hoax. That is where you go wrong. It has been said many times here that extraordinary claims need extraordinary evidence. People who are educated and work in this field do not believe the landing is a hoax, so in my mind to be convinced it is a hoax would take a considerable amount of proof. I have looked at at the evidence and it is lacking. On almost every point there is a explanation that seems valid to me.
I think people believe it because they distrust science and scientists in general. That is a huge mistake to me. What do you think those people are doing for six years or more in higher education, playing tiddely winks? They study that long because it's complicated and hard. They are taught to look at facts and evidence and think critically. Anybody can make a theory and put it on the internet, but it doesn't mean it's a valid theory. Scientific information is peer reviewed and rigorously tested and challenged, conspiracy theories are not.