Something doesn't have to be correct or honest to be an ideology. It's a shared doctrine among a significant part of the far right that "protection of the environment" is their purported motivation for exterminating undesirables. That's absolutely an ideology, even if they're wrong about its effects or even dishonest about it. I don't believe it's all said cynically and knowingly either, and I don't think that Michelle Chan, in that quite accurate quote, is saying that they never believe in the stories they're telling themselves about it. Just that the deeper cause for their actions is actually white supremacy. It would be like saying a religious ideology wasn't an ideology just because it's motivations are not the actual existence of some supernatural entity but instead cultural forces, bonding, the comfort of rituals etc., and I don't think that makes much sense.