I should have mentioned this one too, yeah. Some of their stuff is outwardly “important” and others are like the grunge-y list proffered by the OP, where they just scream and rant about things they think are important in an earnest way but you can’t make head or tails from them from the lyrics, but the OP’s wife is bound to like them 
Thanks for the suggestions so far everyone!
About The Flobots, when I mentioned them my wife recalled that she had heard them and has enjoyed listening to them. But she got kind of aggravated when she heard a line having something to do with “splitting the atom of a molecule.” She says, “I’m a science teacher. I can’t let that go.” 
But having been reminded of the band, she reports that, yes, this is a band from more recent times that she does tend to like.
Half the time I put on KROQ, they’re playing a Linkin Park song. The guy seems to have issues with his dad, judging by the lyrics of their songs. Yes, he does yell sometimes.
The Thermals tend to sound pretty angry and shouty.
Well, here’s something that probably fits the bill: Texas Hippie Coalition’s Pissed Off And Mad About It from 2008. 
Serj Tankians solo debut Elect the Dead would seem to fit the bill (though I’m not sure it’s all that ‘important’) – how does she feel about System of a Down in general?
I’d never heard of Blood for Blood until two days ago, when I stumbled across a Youtube video made by Pat Dollard and a few Marines set to the tune of “Ain’t Like You (Wasted Youth II).”
http :// www. youtube.com/watch?v=zGeWfmqE2HY (Totally NOT safe for work!! Or the library. Or in front of your mom!)
Summed up my feelings in high school quite succinctly. I don’t agree with that attitude anymore, but I sure as hell understand, and we’re going to have to deal with the fallout from those perceptions which are held on both sides of the political fence sooner rather than later.
Worst vocals ever. And the lyrics are themed around Imperial Russia, so not exactly important.
I think Green Day’s “Holiday,” which I really like, fits the bill: http://www.youtube.com/watch?v=pFim5S0_fTc
Loves the sound, hates the lyrics.
Linkin Park? I mean it sounds like Rage Against the Machine is pretty much the template for what you’re looking for. Do kids listen to angry political music these days?
Oh…duh…Green Day.
How about The Falcon?
And I know this is waaaayyyy before 2000, but you didn’t mention Minor Threat as one of her favorite bands and I think of them as pretty much Ur-Shouty-Angry music.
She might be interested in Nothingface (who feature more screaming in other songs on Skeleton, the album that the linked song is drawn from).
Psychostick gets two out of three. Two Ton Paperweight is a good one.
I was going to mention the Flobots, but it’s been done. They do an amazing live show, btw.
That’s a very understandable position – sadly.
The Foo Fighters may also fit the bill. Some songs, like Monkey Wrench have some yelling.
What? No-one listens to SOD for the lyrics anyway. Their sound is unique, not their lyrics. This goes for just about any heavy music these days.
The music cynic in me would congratulate your daughter on having taste.
Seriously though, the music of this decade seems less “angry about important things” or “yelling” than the last decade. If the 90s were musically defined by the sound of Nirvana and Pearl Jam, I’d say the 2000s were defined by the sound of Coldplay.