Burn's reasonably easy to hate out, but there still isn't enough of it piloted by good players that it's worth worrying about for most people. People are probably more worried about Reanimator and Dredge, who consistently make it to the top tables and have a common weakness, and their concerns are IMO well justified.

Saying that Burn is the next Goblins may be going a little too far. Goblins was like Zoo: an aggro deck that dominated metas for quite a while. As far as I know Burn's had good success, but not nearly on the level of these other decks. Have we ever seen two Burn decks in the top 8 of a large event? I'd be surprised if Goblins or Zoo didn't achieve that multiple times during their peaks. (I don't keep too good of an eye on event results, so I may have missed something.)

Anyway, options are limited. For hating the hate, Anarchy, Chaos Warp, Nevinyrral's Disk, Ratchet Bomb, or a splash into green or white. Alternately, and depending on the hate seen, simply using more creatures and nontargeted damage like PoP, Flame Rift, and Volcanic Fallout can work. Uncolored damage sources like Barbarian Ring help.

For Lifelink, Sulfuric Vortex and Smash to Smithereens (or Shattering Spree if you're worried about countermagic) can usually remove the sources.