In my experience (as a reviewer of a peer-reviewed journal) I believe nowadays journals more often than not include a double-blind peer-reviewing process. In principle, a reviewer should leave aside any personal interest and strictly review a manuscript based empirically-derived research (even in those cases where a single-blind process is held by the journal). This, I believe is the basis of development of scientific knowledge. Normally the basis on which reviewers are invited by a journal to review is that of the researcher's experience, grasp of the topic, and a sense to detect whether the manuscript meets the journal's guidelines and if such manuscript is scientifically-sound. Therefore, in practical terms it is very difficult to disqualify (if not impossible to disqualify reviewers) as this is an "Ethics" issue. I suppose I would try to get additional feedback from more peers on my work (if I strongly felt I have a point) and see what other experts think about it, even if this meant submitting my manuscript to another journal. My take is that in the end I would like to get the most constructive feedback to improve my manuscript as much as possible.
Many journals actually let you list the people you do not want to review your paper. However, the final decision as to who will be the reviewers of your article is usually up to the editor handling your paper, who in general is under no obligation to respect your suggestions.