Well, some of the storm-like cards are best stopped with Stax strategies. I mean, Rule of Law shuts down storm and rituals, but it's very Staxy. But it does turn storm and rituals to dust. (Which is, ahem, perfectly balanced, as all things should be.)
You can't really shut down graveyard exile, except by removing it.
tl;dr: If you try to stop Stax, you enable combo. Magic's weird. The things Maro insists are unfun are also the only things that stop turn-1 wins in eternal formats.
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Card advantage is not the same thing as card draw. Something for 2B cannot be strictly worse than something for BBB or 3BB. If you're taking out Swords to Plowshares for Plummet, you're a fool. Stop doing these things!
how do you define group hug, by the way? and stax? To me, they aren't necessarily the opposites, but i can see how some might see it that way. My group hug builds are very player-aimed effects, and not global effects. in my meta, playing group hug basically enables the better decks to 'go off' first. So my group hug gives resources to the slower players and taxes the faster decks.
If your idea of group hug is double everyone else's resources, then sure, that and stax are kinda opposite. I'm not sure how it'd be possible to go around it. Maybe a group stab instead of group hug?