The same thing we've always done: pattern matching based on characteristics with fuzzy boundaries. Cladistics is useful as a way of classifying things for biologists, but not very useful in day-to-day life. e.g. if someone says "let's go sit under those trees", or "let's chop down some trees for firewood", replying that there is no such thing is a tree is not a very useful response.

We don't have these arguments about bipeds because we never assumed that all bipeds shared an exclusive bipedal common ancestor.

I think the best alternative is to use different names depending on what we're highlighting (cladistics versus functionalism, for instance).

The -id/-ine suffix (e.g. ursid / ursine) seems to do this.

It would be clarifying to distinguish hodgepodge groupings such as "fish", and groupings such as "ducks" that are basically monophyletic with some exceptions removed from the group. Ducks are just small Anatidae.

Probably something along the lines of “if it quacks like a duck then it’s a duck”