What you need to think about is what consequence any of this has to your life. The reality is, like the moon landing, it means absolutely nothing to the decisions you'll be making whether it's real or not. Like holocaust denial, the only reason people make one claim rather than another is to be seen as a certain type of person.

To me honestly it appears that the consequences of such beliefs are relevant. If the WTC went through a controlled demolition, this affects the standard view of what happened next, and should influence your beliefs on politics and terrorism at least. This can be relevant to evaluate what to expect from the future and should influence some future decisions. The moon landing is less relevant, but it still says something on the limit of what humanity can achieve under a strong pressure, and can be a factor if extreme conditions manifest in the future (e.g. a huge impending natural disaster). Finally, the holocaust is one of the strongest arguments against dictatorship and expressions of racism. If it didn't happen, your priors against a dictatorship being a good form of government should be modified.