Does the Goliath's carrying capacity increase from its Powerful Build feature stack with the Barbarian's carrying capacity doubling from its Bear Totem feature? For example, would those two together give a character with Strength 20 a carrying capacity of 1200 lbs?
Yes, these abilities should stack fully. While previous editions had rules around stacking multipliers, 5e doesn't, and even if it did, Powerful Build doesn't directly multiply your carrying capacity - it just makes you count as Large.
Your carrying capacity as a Str 20 character = 20 × 15 = 300.
Then being a Large creature (from Powerful Build) doubles your carrying capacity to 600.
Finally, the Bear Totem feature doubles your carrying capacity to 1200.
This isn't particularly imbalanced - you had to work reasonably hard to get it, and carrying capacity doesn't matter that much anyway. Besides, it's not enough to let you beat the Elephant :(