I think it was because #BLM belies a much more complex political movement than the face-value meaning, while #5DemandsNot1Less directly referred to 5 specific things.
This meant that supporting #DemandsNot1Less implicitly meant you supported its specific tenets. While on the other hand, Supporting #BLM was more complex, where many people would absolutely support the literally meaning, but not necessarily all of the rest of the political goals. This makes it easy to attack critics of a particular BLM political goals as if they did not support the literal meaning.
In that context it it easy to understand why the author drew a line between the two memes. Of course that was their opinion, and opinions differ. The author wasn't advocating that everyone have the same opinion on specific memes, they were arguing that such opinions should be informed & critically examined.
They weren't saying "Here's a formula to discover which memes are bad." They were saying "Here's a method to help you come to your own well-informed opinions on the them."