First and foremost, the comments may be right that this question is being asked with the ulterior motive of promoting a product, but it is nevertheless true that hydrogen peroxide and other oxidants (AKA reactive oxygen species, or simply ROS) are potent antimicrobial agents, so I'm going to attempt to answer this question concisely.
I only study immunology tangentially, but my studies on aging usually overlap with immunology due to the role of reactive oxygen species (ROS) in diverse cellular pathways, including DNA damage, protein folding, and immunology.
The ROS produced by organisms (particularly hydrogen peroxide, peroxide radicals, and superoxide) aren't "selective" antimicrobial agents any more than bleach is. Both endogenous ROS and exogenous oxidants like bleach will attack (oxidize) any sufficiently strong electron donor:
ROS act both directly and indirectly to promote immunity, ROS are produced in many epithelial tissues constitutively (i.e. independent of infection) as well as in response to infection by pathogenic organisms. The detection of pathogenic organisms is cell-dependent, and immunological signaling pathways determine whether or not ROS production is appropriate; this is one mechanism by which ROS can be used "selectively" against microbes. On the other hand, innoculation with non-pathogenic microbes can be sensed through immunological signaling pathways at the cell/tissue level and can result in a reduction of extracellular ROS production below constitutive levels to allow colonization by symbiotic microbes:
Yang, H., Yang, M., Sun, J., Guo, F., Lan, J., Wang, X., & ... Wang, J. (2015). Full length article: Catalase eliminates reactive oxygen species and influences the intestinal microbiota of shrimp. Fish And Shellfish Immunology, 4763-73. doi:10.1016/j.fsi.2015.08.021
This article describes this phenomenon in detail, while giving a brief introduction to the other relationships between ROS and immunology that I mentioned. I should stress that this phenomenon is probably not the primary determinant of the effectiveness of ROS as an antimicrobial agent; your comment about microbes with negative reduction potentials is more relevant, although not precisely correct.
The net oxidation/reduction potential of an organism has less to do with the effects of ROS and more to do with their resistance to it. Even if there are plenty of reducing agents (AKA antioxidants) around (NADH-dependent enzymes, reduced glutathione, thioredoxin, etc.), proteins and lipids can be temporarily or permanently damaged by oxidation. Even if antioxidants are available, this damage can overload the cell's capacity to quickly reverse the damage, or even temporary damage can send pro-death signals by disrupting proteins/lipids involved in cellular signaling (see wiki article on bleach). See the following section of the wikipedia article on antioxidants (and its references) for a more thorough understanding of the interplay between a cell's antioxidant capabilities, it's production of ROS, the accumulation of oxidative damage, and the effects of oxidative damage:
Ultimately, a microbe's ability to tolerate temporary oxidative damage (a complex phenotype to explain) combined with its ability to rapidly reverse oxidative damage (based on expression of antioxidant enzymes, accumulation of glutathione, and cellular oxidative metabolism) are the primary determinants of a microbe's resistance to ROS - which is the more accurate way to describe the concept that ROS are (weakly) "selective" for certain kinds of microbes.