This is an interesting subject really. There is certainly a shift in society where people are more sensitive about things and more likely to take offence about things that they simply wouldn't have done even 15-20 years ago. Indeed, there are definitely some people who choose to take offence easily. There is also a shift that sees more people claiming that it is their 'right' to have or do certain things even if that is to the detriment of people. Another unpleasant strain you see you running through society are those people who 'tell it how it is'- no, you're just rude. As a whole, I think we have become more selfish as a society, more concerned with appearing to be successful, and more concerned with being able to do what we want to do and to hell with everybody else.
In contrast to that, we do appear to have made some good shifts. People are now more aware of mental health matters (although other aspects of modern life aren't helpful to people's mental health) and, for the most part, society has become more accepting of other people's sexualities.
However, despite many prejudices being broken down, I think we are less pleasant, more unkind, nastier society than we used to be.
There are some precious little snowflakes out there. Being nice, being kind, being considerate doesn't make you a snowflake though. It makes you a gentleman.