Here's my take on it.
Isaiah 66 is about the years just before and including the beginning of church age and Gentiles coming to God in the church, with Israel promised to come back into the church as well which was promised in
Romans 11:26.
God was restricted to Jerusalem in the old covenant. But THE NEW JERUSALEM is the church --
Heb 12:22. This is speaking of NEW JERUSALEM, the church. Gentiles came into the church in
Acts 10 and ever since. Verse 12.
The holy mountain in Jerusalem is ZION. And ZION is also spiritually speaking of the church, again in
Heb 12:22.
This whole chapter seems to be speaking of the time of Israel after they returned from Babylonian exile when they would lose their heart's faith and sink to mere ritual and idolatry again, and on into the days of the New Covenant.
Their sacrifices would be no better than offering a dog in those days. Herod also came along later and fixed up the temple and built a glorious edifice after those days, which was the temple in Jesus' day. So, the context speaks of the destruction that would come upon that temple in the generation who killed Jesus. And the salvation of Gentiles would occur in the New Covenant.
It was the beginning of the times when Jesus soon came. The state that Israel was in with its pharisees and hypocrites. Then it shoots ahead to see Israel return to God as noted in
Romans 11.
The first verse speaks of heaven being God's throne and earth his footstool, as though it referred to a time when they would rebuild the temple that was destroyed by Babylon. They were entrapped in ritual and outward observance.