From what I understand a species concept is essentially a testable hypothesis; that is, the concept defines a species by describing certain attributes that, when tested against, provides the worker with an indication as to where it fits within taxonomic rankings. So the aim is to remove, as much as possible, subjective decisions from the worker. The criteria is hence 'operational' because it describes series of actions for achieving a result.
I agree with you here; there is really no way to make the naming of species objective with a singular species concept. Life is so variable and ambiguous that it is conceptually impossible. I think that it is possible to make it objective though; we simply need to apply species concepts (there are over 20 of them remember) such that the operational criteria can actually be used. The biological species concept (which is what most people have described in responce to this post), for example, is hopeless when used to demarcate asexual or selfing populations. Why not restrict this concept, which is at the end of the day a nice concept, to taxa for which it is appropriate and thus use its operational
criteria. I think the only reason why taxonomy is subjective is because we assume that a universal concept is possible; and because of the ad hoc usage of species concepts.
Maybe instead of trying to develop a universal species concept, we should instead try to develop a universal means to apply the myriad concepts we already have - all of which a perfectly valid (although some can be synonymised) when applied to the appropriate life forms.