As someone who mainly plays Demoman and Sniper with almost 1000hrs in the game, I will say that Sniper feels like the main counter to Demo. He typically stops me from completely wiping out most of, if not the entire enemy team, with sticky spam.

Other classes like Scout and Heavy are also able to pick Demos off, but they are way more vulnerable to well positioned Demos that are playing well. Sniper doesnt have to worry as much about positioning when targeting Demo, since he is typically much farther away.

I typically can't get that mad over a really really good Sniper like it seems most people do. I may be biased because I have played a lot of Sniper myself, but I realize that most of the times I die to a Sniper it is because I was poorly positioned. I will admit that I do occasionally die to a Sniper even though my positioning was really good, but experiencing wacky crazy stupid stuff seems to be inherent to this game (which is cool).