It is a fair question in general. The answer is: somewhat. Or sort of. That is, whether I agree or disagree with a student's dissertation should have little impact over whether I think it merits a PhD. A dissertation is a serious and original investigation of a significant question. Is the dissertation a contribution to science? I always found that question a bit intimidating and a bit pretentious, but very much appreciated the pro-dean experiences I had at McGill where the hard scientists did very clearly elaborate their contribution to science. Whether I agree with the conclusions and implications is almost entirely irrelevant. The evaluation depends on whether the question is important, whether the methods chosen were appropriate, whether the research design was well-executed, whether the findings derive from the research, and whether the implications derive from the findings.*
* By the way, no one ever trained me on how to supervise a dissertation or what the criteria should be. Ooops.
To give you the clearest example, one of the first dissertations I supervised at McGill targeted my work directly. The student was out to prove me wrong. I surely did not agree with the conclusions, but did not mind the effort to prove me wrong (hate me if you want, but just cite me). Science, even or especially social science, involves conflicting ideas and complex realities, so a well-executed piece of research may not convince me to change my views but it probably influences how I think about things.
Most of the rest of my dissertations students worked on stuff that was largely unrelated to my work, so some produced understandings of the world that convinced me and others not so much. But I approved of them via my signature on the various forms because I found them to be well executed investigations of interesting questions. Would I sign off on a very racist dissertation? Probably not because I doubt that it would have the necessary ingredients--well articulated question, logical theoretical development, good research design, and so on. On the other hand, I did supervise a dissertation that might be read as advice for potential miltias about the strategies one chooses to get support affects one's likelihood of surviving attacks.
Of course, the really important thing to know about Political Science dissertations is that they are long, longer than nearly any other field. But that is a topic for another day and another post.