Social media must take much of the blame (and it's one of the reasons I don't use it).
Nevertheless, I believe there are deeper cultural reasons at its root. For many reasons, people today have less resilience than they did half century ago and even less than the prewar generation.
These reasons are many and diverse and it's hardly possible to detail them here in any comprehensive way but some are very obvious.
First, there's not the same emphasis on teaching manners and self-restraint as there was, say, five decades ago. Nor is the same level of emphasis placed on listening to others and making an effort to understand and accommodate their views as there once was.
Similarly, there's a righteous sense of self-entitlement that once wasn't there to the extent it is today.
And then there's the overprotection bubble that kids have been brought up in over the past forty or so years - for instance, kids being driven to school, and or not being allowed to discover the 'bad' world for themselves. This breeds timidity and an over sensitivity to worldly knocks and thus people now overreact at the slightest provocation - even when they experience the mildest indignation or upset.
Couple these issues with the ever-increasing number of groups of people who consider themselves disadvantaged in comparison to others and we've a recipe for trouble. Having to make 'allowances' and or special rules for so many subgroups of people - whether or not these groups have legitimate or reasonable claims - is wearying society. (Here, I'm not suggesting these groups don't have a legitimate cause, rather it's the effort that society has to expend in adjusting to and accommodating them that's a major source of problem.)
Then there's other factors such as inequality which is growing so fast that people haven't time to adjust. Same goes for racism, mix too many different ethnic groups too quickly and or that the population growth rises too quickly so people don't have time to adjust and the discontent manifests as resentment towards others.
Put all this together with a media that squawks loudly at the slightest provocation and you've conflict for sure.
It seems from the evidence that Fry does have a valid point, how relevant it is remains to be seen.
Incidentally, decades ago when I was growing up and copped abuse from others, I was taught to consider the old ditty 'sticks and stones may break my bones but words will never hurt me'.
From my experience, there's a modicum of truth in that saying.