As you can see, the question asked whether respondents thought that universities should a) protect free speech even if that meant allowing offensive and racist comments or b) making sure students have an environment free from discrimination even if that means limiting what students can say.
As you can see, there are fairly dramatic differences by political orientation. Democrats were significantly more likely to not endorse free speech and were significantly more likely to endorse limits on free speech for college students compared to republicans.
Methodologists will likely quibble with how the questions were phrased but I believe they adequately capture core differences between these groups. Research tells us that liberals--and I realise not all democrats are liberal--prioritise equality. Haidt, moreover, also tells us that liberals have made sacred certain ideals. One of these ideals is the protection of minority groups.
The questions contain a reference to racism, thus pitting off competing values between supporting free speech and protecting minorities. Framed this way, it is pretty clear that democrats value the protection of minorities much more than they value free speech.
Let's assume that these findings are reliable and that they generalise to democrats and republicans at-large. I think they may help to explain why we see so many efforts to curtail speech on college campuses. The vast, vast majority of university faculty are democrats and are, by any measure, further to the left than "average" liberals.
When free speech is framed as a competing value in opposition to the protection of minorities, free speech loses and justifications to limit speech follow.
It would be nice to see if other questions were asked that juxtaposed similar values. Do democrats, for example, support free speech under some conditions but not others. Same thing for republicans. Do they support free speech under a broad array of conditions or only those outlined?
At any case, these findings also tell us why intellectual diversity is important. Most academic departments in the social sciences and humanities don't contain a single republican--people who bring a different set of values to the table. In this case, they tend to support free speech.