I don't get the argument referencing the lack of gameplay shown in this trailer: TLOU had cutscenes, the sequel will do too, and they've used one cutscene to establish the tone of the world whilst showing off the graphics. This approach isn't new and, given that Days Gone has shown a fair amount of gameplay so far and both games share a similar premise, I think it's a wise move to limit all gameplay footage to the title likely to release first.
As for the violence: I don't see the issue. Fair enough if it's not for you and you'd rather play something lighter, but the world of TLOU was established in the first entry, and the tone, the brutality, and the horror of this trailer was appropriate to it.
This isn't the cinematic version of World War Z (I hear the book's quite different,) this is a cruel, bleak world where the worst of human nature dominates, and one of the few games with a genuinely interesting anti-hero, for whom you cheer in spite of his moral shortcomings. "...it's okay, I believe him."
If this was the trailer for the next Legend of Zelda, I'd share the disdain. But it isn't and I don't.
And just as I pass on romantic comedies because they bore me to tears and tire my eyes from rolling them so much - not to mention the fact that every character that you're supposed to care for is wildly immoral - people who feel the same about "gritty" content should do the same here.
That being said, I'm also tired of the more general move towards gritty and away from fantastical, but I feel Uncharted 4 is more representative of that. TLOU2 seems perfectly in-character.