A behavior, no matter skin color, is a defining factor for me. So whether I call a black man a thug or a white man a hillbilly or vice versa, I'm not generalizing an entire race. But you can't deny there are specific groups of people who can be attributed to these labels.
I think the problem is that you are separating thug and hillbilly into two separate sort of negative labels, and you are applying them to race. Yeah of course, there are obvious connotations to each of these labels, and they may be useful summations if you want to describe particular behaviours - but I think this ends up evolving into something even more negative.
I feel like eventually these labels become these large and unwieldy clubs used to discredit, and they end up further becoming more deeply entwined with ethnic bashing.
I'm not always very coherent, so I'll try and describe it as best as I can, but let me use thug as an example (mind you, I'm black, but I haven't really had a lot of experience with this word as an insult, I just don't think it's vogue in my circles I guess): So you want to describe a group of people you've recognized who are violent, unintellectual, and maybe often dress very similar (poorly, lets say). Thug is the word you use and it is a quick and simple way to describe someone - we do this sort of thing all the time, it's not particularly weird. Now eventually this evolves - thugs wear baggy pants, thugs live in the ghetto, thugs are black, thugs do drugs, sell drugs, steal, rob - etc etc etc etc. Both the physical description (used for recognition purposes) and the nefarious things thugs do grow as people adopt this term and add to it as they see fit. Eventually it becomes less of an ambiguous description and more of a universally held negative. "Oh he's a thug? I know immediately what you mean, and all the negatives that come with it". Now this word is a powerful tool, it's not just a general description of some fuzzy observation/trend - it's a direct and powerful insult/accusation that carries with it a lot of hidden connotation - because people have built it up to be larger and larger and eventually this... racially charged thing.
You might not have seen it, and I haven't really seen it directly myself, but the internet is a wonderful place that has given me plenty of access to things I don't normally see - like people who use thug just to describe -any- black person. It's not just a label they ascribe to just people who meet a bunch of criteria, but they'll happy apply it to anyone who meets any of the criteria - often with a heavy emphasis on the ethnic criteria. What originally was a very specific description with a lot of requirements (baggy loose clothing, violent, unintellectual, angry and aggressive, etc etc) is now used by some people on anyone who is black - with all the negative connotation still intact. Maybe it's not just them being black, maybe it's them being black and wearing baggy clothing. Maybe it's them being black and talking loudly and aggressively - they might need one other slightly relevant bit of information before they're willing to apply the label. So when they do, the requirements are much diluted, but the implications are not - the implication is still that thugs are anti-intellectual, angry, violent, no-good etc etc's.
So I guess what I am trying to say is, I can understand why the label, why all labels like these, can turn into what are essentially slurs. Maybe a good amount of people still use thug to mean a very specific sort of person, but the damage is sort of done. Sometimes now when you use the word thug, you'll be in some way (to some people) associated with the sort of people who use the word thug without meeting all the criteria.