Isaiah 39-66

Isaiah 56:6-7
Also the sons of the foreigner
Who join themselves to the Lord, to serve Him,
And to love the name of the Lord, to be his servants --
Everyone who keeps from defiling the Sabbath,
And holds fast My covenant --
Even them I will bring to My holy mountain,
And make them joyful in My house of prayer.
Their burnt offerings and their sacrifices
Will be accepted on My altar;
For My house shall be called a house of prayer for all nations.

Hey, look! The Old Testament God is talking about the salvation and righteousness of gentiles!

58:6-8
Is this not the fast that I have chosen:
To loose the bonds of wickedness,
To undo the heavy burdens,
To let the oppressed go free,
And that you break every yoke?
Is it not to share your bread with the hungry,
And that you bring to your house the poor who are cast out;
When you see the naked, that you cover him,
And not hide yourself from your own flesh?
Then your light shall break forth like the morning,
Your healing shall spring forth speedily,
And your righteousness shall go before you;
The glory of the Lord shall be your rear guard.

People like to talk about the Old Testament God and the New Testament God (as i facetiously did above). The truth is, God is God. "I am that I am." Remember that the Bible was written by human beings, who were influenced by the culture and time period that they lived in. I had a class in my freshman year where the professor (now my pastor) used to remind us every day that the things we say about God reveal a lot more about us than they do about God.

So the things that the authors of the Old Testament said about God said a lot more about the authors than they did about God, and the same goes for the New Testament. That's why it's important to read the whole Bible, multiple times, and to talk about it with others, and read commentaries and scholarly works on it: it is still possible to learn truths about God from the Bible, but you've gotta take everything in it with a grain of salt.

This passage, however, is a good example of how God's nature is eternal and unchanging. In fact, all of Isaiah is a pretty good book to read to help people untangle their understanding of OT and NT God. We see God repeating Himself a lot, and those messages are generally good ones to pay close attention to.