Is it legal for a publicly-funded institution to ban a certain pattern of speech?

Do you believe a public college or any other public institution has the right to regulate your speech code as it sees fit. After all, black supremacists and KKK members pay taxes too. Why would you be forced to take certain classes for not living up to a certain group's standards of tolerance. I think no public institution should be regulated with respect to speech. I'd love to hear other views, preferably from legal experts and people who are willing to be unbiased in their answers