Do social classes hang more with the same social class?
If we take "social class" to mean income/wealth as it's most commonly the case in the West today, then there's even an academic term for the uncommon friendships across such classes, namely "income-bridging". As for their occurence, let me quote you from a paper by Léna Pellandini-Simányi (which happens to survey Hungarian society, but I think it easily generalizable across the Western world):


  Many of the income-bridging friendships are between former classmates whose class position diverged, yet who kept
  their old friendship alive. 


Let me tell you from personal experience that this is 100% the case for me, if we take the "income-bridging" to mean a tenfold difference in income. 

Also from the same paper on Hungary, this interesting bit regarding the socialist past:


  During socialism, status-bridging friendships were not more frequent in
  Hungary than in capitalist societies, contrary to the image of an egalitarian and open society promoted by political public discourse. [... However] It is important to note that these [socialist-era] studies measured class by education and working position, omitting income.


The last part kinda reminds me of joke/advice along the lines of: don't get a PhD to impress your friends, once you get a PhD most of your friends will have one.