IMO, all misunderstanding of Lumen Gentium results from seizing upon one particular image -- such as People of God -- to the exclusion of the others and without reference to the divine radical unity of the images.
Yes. The problem is one of studied ambiguity and taking the terminology of out any coherent context and playing around with all sorts of bizarre liberal and leftist interpretations of metaphorical language. The "people of God" quickly becomes "the people's assembly" and "the People's Church" with even Marxist overtones. Then any group of liberal lunatics can claim they are the "People of God" who know best what the "new Church" should look like.
A similar phenomenon happens with the language of "The Church in the Modern World." The term "modern" gets injected with all sorts of silly meanings including the idea that ridiculous "modern" architecture should become the norm for church buildings. It's an anything goes mentality.
If you listen to the way some dissidents speak, they talk as if everything "Catholic" must be replaced with some new "modern" version - modern music, modern theology, modern architecture. It's quite silly.