Moderates oppose changes that cause drastic shifts if there is doubt as to the proper course of action to take. That is not a point against them. It is not about holding onto tradition, but rather untangling the opposing viewpoints to understand the core of a problem.
That doesn't mean that moderates do not support causes or fight for what they believe is right. However, a moderate would disagree with joining a radical political movement. Dogmatic alignment with an ideology does not result in progress.
If one side of the spectrum is wrong, a moderate will side against it. However, in politics, neither side is right or wrong 100% of the time. Forcing compromises and understanding opposing viewpoints is how allies are won. Examining the cause and effect of actions is fundamental to ending up on the right side of history.