As @thomaseverest mentioned, we need to separate the discussion of conservation status and establishment means. Conservation status is inherited in a cascading way from higher taxa, whereas native status is not. This makes sense, as many species have subspecies, and in the majority of cases, those subspecies are allopatric or parapatric, so inheriting native/non-native status would not make sense. This feature request, then, is focused on conservation status.
In terms of conservation status, assessments are usually made at species level (e.g., on the IUCN Red List), although exceptions exist for well-known subspecies (e.g., primates) and for subspecies on national or subnational red lists. That means that by default, the most common level at which conservation status will be applied is at species level, even where subspecies exist.
I think this issue can perhaps best be dealt with through better display showing at what level the conservation status was applied. So on the taxon page, it would be useful to separate inherited conservation status in a different section from those applied directly to that taxon. We can discuss whether taxon-level conservation status should always take priority over inherited, or whether it should be the most threatened that always takes priority. The latter is the case at present, as far as I understand, which leads to some odd behaviour such as the domestic rabbit subspecies being labelled as Endangered because the species as an entity (based on its wild, native populations) is Endangered, even though the subspecies conservation status has been set to Least Concern.
In a case like this, I think it should be made clearer on the observation that the conservation status is from a higher taxon. Instead of saying “Conservation Status: Endangered (EN) (IUCN Red List)” the tooltip could say something like: “Conservation status inherited from higher taxon: Endangered (EN) (IUCN Red List)”. The words “higher taxon” could be linked to the higher taxon page, or be replaced by the name of the higher taxon.
Similarly, on the taxon page itself, it could be made clearer in the banner at the top of the page that this status was inherited from a higher taxon. For now, it says: " “endangered” Globally (Source: IUCN Red List)". It could read exactly the same as the tooltip text: “Conservation status inherited from higher taxon: Endangered (EN) (IUCN Red List)”.