I agree that correlation doesn't equal causation, but the correlation between the degree level voters is very high, it doesn't "drop off" all that much after university, but drops off with age, where older people are less likely to have attended anyway ( 5% of those who were born in the 1940's/50's rising to 15% of those born int the 60's) its actually fairly easy to look at the vote trend and find that there is a significant correlation between the two and so therefore level of education is a significant determinant of the way that you would vote.
There is also a significance that areas with more highly paid , educated and professional workers voted in the majority to remain, whilst those with low paid, low skilled workers voted to leave, further demonstrating the links mentioned above.
I think the condescension shown to leave voters comes from the fact that leavers often use reasons that have been proved to be based on incorrect information tome and time again, yet they still use them.
Many of my friends do not have degrees, but they don't demonstrate this sort of ignorance, or unwillingness to admit that whilst the information was out there, they chose to only look at flawed sources which confirmed their own bias.
Its fine to critique people's opinions and to challenge them, the everyone's opinion is equal narrative is not correct and merely allows the further expansion of post truthism.