Once you have actual organized NIMBYism, you are selling to existing property owners and residents. They have no real reason to "buy" this story. Either low cost housing doesn't affect anything, or it is against their interests. In no scenario does benefit them, so why shouldn't they object... just to be safe? At the least, construction is noisy and unsightly.
I think NIMBYism should be accepted as-is. Existing housing has an interest in preventing new housing by default, especially down market of them. That's how organised NIMBYs see it. That's how it plays out in practice. YIMBYs are not going to beat NIMBYs locally.
NIMBYism exists. The relevant questions are about how to build despite of NIMBYism, not how to reason with it.