EAD these words carefully: “Can two walk together except they be agreed?" (Amos 3:3). Applying the verse to the principle of separation is indeed reasonable, practical and beneficial. However, in the context of this chapter, it seems obvious enough that the verse here is about God and Israel. If God and Israel were going to cleave to each other in harmony, then they simply had to see eye to eye on things. And, since God's character and principles were certainly never going to change, then we know without a doubt who had to adjust.
It should go without saying that we should walk with God. And, we have many examples of God condescending to our low estate in order to be accessible to us (most observably and effectively in the incarnation of Christ). However, the expectation and accessibility of fellowship (between God and man) only raises the bar and obliterates all of the imagined excuses that can be constructed for not walking with God. Simply put, we can't fellowship with Him if we can't agree with Him, and we can't agree with Him if we aren't willing to be altered.
Now, Israel had fellowshipped with the Almighty at times in their past. And, this just made them more even accountable. "I have known you," God said, "therefore I will punish you for all your iniquities" (vs. 2). His anger was justifiable, of course, but the logic which He used (to convince the Jews of their guilt) may seem a little odd to us. He gave some "cause and effect" examples in nature and then basically said that if He was upset, then they had to believe that He had a good reason to be so (vs. 4-6).