Paper Four in my freshman composition class is a Policy Proposal: students choose an issue relevant to society, and write a proposal to address this issue. This means I get to grade a lot of papers I deeply disagree with.
But I'm ultra-conscious of maintaining objectivity when assessing papers. Because I don't want my own views to color my assessment of the content, I focus on how the student makes the argument. Sometimes the argument contains (in my view) faulty logic, questionable sources, narrow views of the issues, distortion of facts, disturbing ethics, and shoddy ideas. I shake my head at these ideas, then give the paper a grade based on the thesis statement, thesis support, organization, and/or sentence quality.