That is only true if the distribution of things within the continuum is not "lumpy". For height it isn't, but for other things it is. For example gender is highly bimodal, yet still a continuum. Would you say that "male" and "female" are subjective socially constructed categories? Of course not.
Race is probably somewhere in-between. There are people all over the spectrum but there are pretty clear large groups with sparsely populated gaps in-between them.