The glory days of polished, classy celebrities such as Judy Garland and Cary Grant have long since passed. Now we have trainwrecks such as Kanye West and the Kardashians. Social media has made it easy for them to air their personal lives to the public, which means that the less savory facts will also come to light. They are encouraged to act outrageously or shamefully in order to get more attention, and they gladly oblige.
It is not clear what a classy celebrity is. Nevertheless, to the extent that they are extinct it is not because of social media. Social media is nothing other than a different medium by which people express themselves. If social standards and norms have changed with the rise of social media it may simply mean that the previous mediums were not accurately reflecting the social standards and norms.
I don't think that classy celebrities have become extinct. However media outlets are going to give the people what they want. If the trashy celebrity gossip is what's getting the screen time, it's because the website/broadcaster has decided that is what their audience wants to see. I think that classy celebrities are still out there, we just don't hear about them because the stories aren't juicy enough to warrant media coverage.
Through the use of social media, the public has been able to redefine what a celebrity is. Today, people expect their celebrities to be more human. In general, people are more down to earth with each other than they were before. That is true for all people, not just celebrities. Social media celebrities are still classy, just in a modern way.