Are red blood cells prokaryotic?
When differences between prokaryotes and eukaryotes are taught in an introductory biology course, a generic prokaryotic cell and a generic eukaryotic cell are typically compared. Cells in a complex multicellular organism, like a human, are quite diverse. Human red blood cells are one example of a highly specialized cell with a mature form that is quite different from the typical eukaryotic cell. Keratinocytes in the epidermis are another example (see Ross Histology, Ch. 15). In both cases, these cells produce large amounts of a single protein, eventually, at their most mature stage, stopping protein synthesis, extruding their nuclei and most other organelles. 

The absence of a nucleus or other organelles, however, does not necessarily make either of these cells more susceptible to antibacterial antibiotics. Antibiotics are targeted toward things that bacteria have (positive differences), rather than the absence of typical eukaryotic structures. Almost all antibacterial antibiotics have one of three targets (see Goodman and Gilman Chs. 48, 52-55): 


The bacterial cell wall or membrane
protein synthetic machinery
specialized metabolites required by bacteria


There is (almost) no overlap between these structures in bacteria  and structures in any of the diverse array of human cells. The one partial exception is a similarity between the mitochondrial and bacterial ribosome, that may, for example, be responsible for some of the toxicity of chloramphenicol (G&amp;G Ch. 55).