This would give Amazon a huge competitive advantage (given their existing infrastructure). Of course they support this.
It's similar to Walmart's minimum wage support. If Walmart were against minimum wage increases, their opponents would lambast them for it. If they're in favor of it, they get accused of only being in favor of it because they know they can more easily afford it compared to smaller retailers.
Now that they agreed to start paying sales tax going forward (in return for no back-penalties), they are lobbying for their competitors to have to pay sales tax as well.
They are also building warehouses in-state now and trying to compete on speed of delivery, which is a more respectable way to compete against out-of-state rivals.