I completely agree with the precise analysis by @stefkeB regarding the current IfcClassification and IfcClassificationReference support (or lack of, as pointed out by @TLiebich) from applications.
However, I would add usBIM.viewer+ to the list.
It is a free IFC viewer and editor that regarding the classification systems has the capability to take an already existing IFC file (2X3 or 4) and add/update/remove classification information based on common systems (Omniclass, Uniclass, etc.) or to add a custom schema, and to filter entities based on such informations.
More info on another topic here.