Parler agreed to abide by Amazon’s moderation policy and it agreed that it was responsible for the content of its end users.

My landlord has a ‘no parties’ clause in my lease because my apartment is in a factory and someone could be easily hurt if one of the machines turned on. I agreed to this contract. If I break it my landlord is within their right to terminate my lease.

I don't know where you live, but here your landlord could absolutely not throw you out on the street the next day if you throw a party, no matter what the contract says.

Depending on where you live, they absolutely can terminate lease and evict for convictions on a huge laundry list of crimes: violent crimes, crimes that were conducted out of the domicile (especially drug convictions) anything that causes irreparable harm to people or property, etc. even in places with very strong tenant-friendly laws.

Parler hasn't been found guilty of anything in a court of law and given the free speech protections in the constitution, probably won't be, so this sub-thread is irrelevant.

The correct analogy is that a landlord cannot throw you out on a whim because they don't like your friends or your friends get in trouble. And that is true.