Follow-up of Jack's previous post. Biology has long ago set the rules for categorization, trying to capture the elusive but critical notions of taxon and species. Of course, it's always interesting to look at breaches in this system to see how robust it is. Without looking far away in the past to yet unclassified fossils, just consider common practices such as tree grafting and cattle cross-breeding. Interestingly enough, various religious traditions have been extremely touchy about them, often forbidding them merely because of entailed taxonomy breaches, the species organization being considered as the expression of some divine order. See for example this article showing how complex those issues can get in practice when addressed by Torah experts.
Most fears linked to bio-technologies are indeed to be considered at the same level. People are both fascinated and scared about hybrids and GM organisms, as they have always been about monsters and chimaeras of any kind, more for the breaches they make in their world representation than any objective danger they bring about.