It's the single most annoying mindset in existence.
It's annoying because it's completely backwards. Raising one's voice, or protesting, or making noise in some coordinated, intentional way requires infinitely more effort than "not being offended." That act literally requires nothing, other than the optional effort to slap the word "butthurt" onto some low-res google image of a Minion with Elvis sideburns, and cram it in the Facebook comments of the peripherally related news story you've half-read.
This isn't to say everyone who's offended by everything is automatically 100 percent right, and we should never press ourselves into difficult conversations. But the way we talk about these controversies -- where speaking out or protesting is treated as though it reveals some weak, whiny inability to just DEAL WITH SHIT, whereas being uniformly unfazed by everything represents some transcendent strength (or transcendent laid-backness) worth bragging about -- is completely backwards.
Let's take a well-known example: when Notre Dame students walked out of Mike Pence's commencement address last May. Walking out on Mike Pence (or whatever more recent daily/hourly/millisecond-ly example you want to use) takes coordinated effort, and comes with the knowledge that you're gonna get dragged online by every furious 50-something who manages to stumble across your snowflake-tale on some all-caps Facebook page that somehow fucks up the apostrophe-S's in its group name like 11 times. NOT walking out, and just sitting there listening to some guy say inspirational words for a half hour, is a billion times easier. Whether or not you agree with the cause of the people walking out, they were choosing the more difficult option. That's not really disputable. But it's always going to get framed in some circles as, "These poor widduw students got trig-trigged! Why couldn't they be strong and brave like the people who boredly sat there and now aren't getting death threats on their LinkedIn accounts?"