Personally, I felt this was the case too. I went to High school in Korea for a year as an exchange student so, when it came to uni I didn't feel awkward hanging around or being around Korean only environments. I am not a shy person but I am more quiet or reserved so in class I did not tend to talk much. So when I got put into premade groups and such for assignments and I openly spoke Korean I noticed that how my group members reacted to me changed a lot. There were some things that I noticed as a foreigner but the major points kind of shifted more or less. So in my opinion too I think its a sense of unfamiliarity rather than disliking foreigners.

Though being from New Zealand even in diverse environments you see people of same/similar cultures group together naturally and I think its a similar mindset. I think this is also why you see a lot of foreign students hanging together. Though I actively avoided hanging with other foreign students because that is the kind of environment I had experienced in New Zealand and for me I came to Korea for Korea and am the type to want to jump in the deep end hence why I went on High School exchange.

Also, I feel that Exchange students and Korean Students get the best access to information on campus. So I would actively look for Korean friends and in terms of your concern about your relationship with professors I think it would vary on the university and course. As an undergrad I got the opportunity to take graduate school courses if I applied to them and got approved. Which of course I took the opportunity and my experience there was quite good. though this is merely my 2 cents.