It's about as artificial as the concept of 'nations' I feel

Is there such a thing as real taxonomy

in the unlikely case that this is a serious question: yes, there is, at least for eukaryotes.

for eukaryotes (things that have a cellular nucleus) there are "species" which are groups of organisms that can't produce offspring with each other. The reasons are typically (i think?) that the genetic differences between two species are too great and any offspring would therefore have such a self-incompatible set of genes that they cannot live with.

for prokaryotes (bacteria) the situation is a bit different. due to horizontal gene transfer, they can exchange genes with practically ever other strain of bacteria, as long as the environmental circumstances are right. (and the result is often viable, i.e. the resulting bacteria can live that way). as a consequence, there are not so clearly defined "species" for bacteria. however, there are still groups of bacteria that have a higher similarity to each other, so we still group them together and give them names.