Sometimes the rivalries make it even more extreme. Probably one of the most well known is the Michigan and Ohio State rivalry which has been going on for years ad years in football. A few years ago, my dad went to Columbus, Ohio for the Michigan Ohio State game. When he came back from the game he told me about how at one point when he was standing trying to get a better view of the field, an Ohio State fan walks up to him tells him "Michigan sucks," and then punched him in the stomach which my dad said was sore for a couple of hours. Now not all fans are like that, but rivalries make things much more extreme and can cause fans to do some crazy stuff. But rivalries can make things all the more enjoyable.
Perfect illustration of this would be the riot that was the 1980 Scottish Cup football final between Glasgow Rangers & Glasgow Celtic, though that was all to do with religion. I remember watching it live and thinking war had been declared- http://www.thecelticwiki.com/page/1980-05-10%3A+Celtic+1-0+Rangers%2C+Scottish+Cup
I would think for every fan that punches the rival fan/starts a fight/etc., there are a lot more that want to do the same...
Some people do take things too seriously.For example on the other hand we love to beat the Swedes in ice hockey. We can lose to anybody else but not Sweden, that is always a nightmare. But still we could sit down with a Swedish fan after a lost match and have a pint or two. What happens in the rink stays there. And there“s always the next match.
I found this while looking for more on Rangers v celtic Although its www.belfasthumour.com vice guide its fascinating, but not funny nor safe for the easily offended. https://www.youtube.com/watch?v=zqeqXLCREfs