This is a brilliant insight into what's at play here.
As I read your comment I started thinking back on my upbringing, how it connects to who I am today, and how I react to offensive encounters.
I pre-date the internet as it exists today. I still remember BBS being the "biggest thing ever."
Given my age I guess I had what you'd now call a increasingly-bygone era in terms of growing up. My father was the earner, mom was a stay at home mom. After my father died and mom went to work I still had an adult at home, whether it be one of my older brothers, an uncle, whatever.
We had a family unit, and with it a foundation. I had peer groups, and of course was exposed to commercials/corporate branding, but I wasn't raised by it. I was raised by family. There was no always-on, or constant in-hand, access to media. There wasn't a hundred different forms of digital stimuli clamoring for my attention. When I wasn't playing with legos or whatever on my own I was doing things with the family.
Most of my time was spent with the family, including dinner every night at the table. We'd spend dinner going around the table either talking about our day, or some significant event that had been in the news that day. As you do.
Now, as an adult, I find I'm not someone who is easily offended. Not even when people try to intentionally offend me. I know who and what I am, and I just can't be bothered to care if they have something negative to say about it. Their taking issue with it says more about them than it does me.
I find value in those who disagree with me, especially if their disagreement is passionate. For me that's an opportunity to not only learn about their perspective, but also to reflect upon my own. I've learned more about myself from someone disagreeing with me than in any other way.
Oh and trust me, there's a lot of disagreement for me to explore where I live.
I'm a gay, atheist, liberal, socialist, who lives in a deeply Christian and Republican state. My roommate is similarly inclined to me but is pagan and not quite as liberal. Her partner is a god-loving Trump supporter. We all live together.
We're all of the same age bracket, had similar family-oriented upbringing, and we all get along just fine even though there are some deep divisions between our various viewpoints.
I look at the youth of today and imagine them in a similar situation and all I can see is furor between them.
I think you hit the nail on the end, the way children are raised now (lacking what we'd call a traditional/old-school foundation) they don't develop a secure sense of identity that comes from a solid family unit.
Don't take me wrong, I'm not saying the modern family is loveless, fickle, or weak. Just that it's different, and that you're right about both parents having to spend more time out of the home having had a significant impact in regards to the younger generations being thin-skinned.
Then again, this could all be a problem with mistaking correlation for causation. It's interesting to think about, nonetheless.