I think I get the angle here, but the whole thing about a single category/classification/abstraction against a continuum is that it doesn't need to speak to or predict the entire continuum, or to every quality and aspiration of one of its members. One set of things, "those items which have X", need not exclude their members from being in another set which might deal with Y and Z! The concept of a single class, whether we are talking Bertrand Russell or Marx, != complete "taxonomic" classification. As such, a social class is, yes, a lossy abstraction taken from the point of view of any given individual, but it's not like it's failing at being a good category because this is so. That's just, like, how concepts in general work?
I wonder what politics looks like following through with your argument? How do we conceive of things like the "public best interest" if any given classification is doomed to not capture people actually? What is the "public" here? Are there children? Seniors? Veterans?