How do non-trinitarians explain Isaiah 43:11 taking into account its immediate context?

"Non-trinitarian" includes "binitarian", those that believe that Jesus is God, but do not believe that God's holy spirit is a person.

See my answer to contradiction - How can John 1:18 say that "No man has seen God" when the Bible says that Abraham, Moses, Job and others have? - Biblical Hermeneutics Stack Exchange.

A summary is that Isaiah's "LORD" (YHWH), and Jesus were in fact the same person. Jesus was the incarnation of the God of the Hebrew scriptures. The world didn't even know about the Father until Jesus revealed him.

O righteous Father! The world has not known You, but I have known You; and these have known that You sent Me. And I have declared to them Your name, and will declare it, that the love with which You loved Me may be in them, and I in them. — John 17:25-26

This is an excellent question and you've got some nice answers here. I'm not trying to detract from the answers already given, but I'll provide another possibility that's similar to Polyhat's answer.

The basic premise of my answer is this: The most high God sent Jesus as a savior, and that's why He can be called such without contradicting Isaiah 43:11.

Within the context of the OT itself we can see this happening often enough. Here are a few quick examples I dug up:

1. Judges 3:9 (ASV)

And when the children of Israel cried unto Jehovah, Jehovah raised up a saviour to the children of Israel, who saved them, even Othniel the son of Kenaz, Caleb’s younger brother.

2. Judges 3:15 (ASV)

But when the children of Israel cried unto Jehovah, Jehovah raised them up a saviour, Ehud the son of Gera, the Benjamite, a man left-handed. And the children of Israel sent tribute by him unto Eglon the king of Moab.

3. 2 Kings 13:5 (ASV)

And Jehovah gave Israel a saviour, so that they went out from under the hand of the Syrians; and the children of Israel dwelt in their tents as beforetime.

I'm sure there are plenty of other examples in the OT. It would just be a matter of breaking out a concordance and searching on "savior" or "saviour".

But the essential answer is that God most high is the ultimate source of salvation. Without Him there's no saving anyone. He can send someone as a savior and still be the only savior. It's not wrong to say that Jesus is savior because God is in him but we don't even need to go that far. No scripture says that God was in Othniel or Ehud (as far as I know) and they were still called saviors. God simply sent them, or "raised them up", to be used as agents of salvation.

Non-Trinitarian Perspective

Having studied this issue thoroughly for several years, my view shifted from a Trinitarian perspective to a non-Trinitarian viewpoint, so what follows is one person's non-Trinitarian explanation.

The New Testament Agrees

First, it is worth noting that the New Testament also identifies God as our Savior.

To the only wise God our Saviour, be glory and majesty, dominion and power, both now and ever. Amen. (Jude 1:25, KJV)

It also identifies the Father as the only true God (see John 17:1-3; 1 Corinthians 8:6, 1 Timothy 2:5, etc.).

But what about verses that appear to say Jesus is our Savior?

To Titus, mine own son after the common faith: Grace, mercy, and peace, from God the Father and the Lord Jesus Christ our Saviour. (Titus 1:4, KJV)

Look at the prior verse to see the context and explanation.

But hath in due times manifested his word through preaching, which is committed unto me according to the commandment of God our Saviour; (Titus 1:3, KJV)

And in the next chapter:

Not purloining, but shewing all good fidelity; that they may adorn the doctrine of God our Saviour in all things. (Titus 2:10, KJV)

And there are other verses calling God our Savior.

Paul, an apostle of Jesus Christ by the commandment of God our Saviour, and Lord Jesus Christ, which is our hope; (1 Timothy 1:1, KJV)

For this is good and acceptable in the sight of God our Saviour; (1 Timothy 2:3, KJV)

And my spirit hath rejoiced in God my Saviour. (Luke 1:47, KJV)

God is our Saviour.

Why then can Jesus be called our Saviour? It is simple: God was in Christ.

To wit, that God was in Christ, reconciling the world unto himself, not imputing their trespasses unto them; and hath committed unto us the word of reconciliation. (2 Corinthians 5:19, KJV)

The Old Testament Savior

The Old Testament agrees with the New Testament in identifying God as our Savior.

The LORD [Jehovah] is my strength and song, and he is become my salvation: he is my God, and I will prepare him an habitation; my father's God, and I will exalt him. (Exodus 15:2, KJV)

The LORD is my light and my salvation; whom shall I fear? the LORD is the strength of my life; of whom shall I be afraid? (Psalm 27:1, KJV)

The God of my rock; in him will I trust: he is my shield, and the horn of my salvation, my high tower, and my refuge, my saviour; thou savest me from violence. (2 Samuel 22:3, KJV)

The Only Savior

I, even I, am the LORD; and beside me there is no saviour. (Isaiah 43:11, KJV)

Yet I am the LORD thy God from the land of Egypt, and thou shalt know no god but me: for there is no saviour beside me. (Hosea 13:4, KJV)

Conclusion

God is our Savior. Jesus was sent by God and God was in Him. It follows that if God is our Savior and this Savior was in Christ, Christ participates in our salvation, but it is God who saves us through Christ. The Bible confirms this:

Much more then, being now justified by his blood, we shall be saved from wrath through him. (Romans 5:9, KJV)

We are saved by God through Christ.