Given that I'm a complete outsider to this genre (never could get into the old stuff or the new stuff), I don't know how much mileage my opinion gets, but here's my observations. I'd say the changes came around the early '00's when the style was being integrated with several other remaining popular genres of the '90's, namely alternative rock, post-grunge, and pop-punk. From what I've seen and heard, what was considered emo in the early '00's wasn't very similar to the genre of the late '80's and early '90's except the emotionally charged lyrics. One thing that is noticeably different is the sense of style, if you google image search bands like Rites of Spring or Sunny Day Real Estate, you see they don't look like
this. I think that's where most of the disdain comes from, not the music, I'm sure most people that look down upon it have never heard a song, but they see people that fit the stereotype all over the place and then make their assumptions on the music by that.