Why would God want his people to build tabernacle and the sacred rooms, only to destroy them after Jesus dies on the cross? Does that mean God has changed his mind?
This is a really interesting concept in Christian theology, known as typology. Essentially, it is a method of interpreting the Old Testament as a long series of "types" that prefigure aspects of the revelation in Jesus Christ, which are known as "antitypes".
This is mentioned in the Catechism of the Catholic Church:
The Church, as early as apostolic times, and then constantly in her Tradition, has illuminated the unity of the divine plan in the two Testaments through typology, which discerns in God's works of the Old Covenant prefigurations of what he accomplished in the fullness of time in the person of his incarnate Son. (CCC 128)
For instance, we might look at the story of Jonah, which is commonly read in Christianity (especially in mediaeval Catholic and Orthodox theology) as a prefiguring of Christ's death, three days in the tomb, and resurrection. Similarly, the serpent lifted up on a pole by Moses in the wilderness in order that those who look upon it might be saved (Numbers 21) is read as a type of Christ's being lifted up on the Cross.
However, the example you mention in your question is possibly the canonical example of typology. The Temple, the dwelling-place of God, is understood as a prefiguring "type" of Christ, in whom God dwells on earth. The sacrifices of the Old Covenant are considered types of the one great sacrifice of the New Covenant, that of Jesus Christ on the Cross. The priesthood of the Old Covenant is considered a type of Christ's eternal high priesthood. If you read the Epistle to the Hebrews, you will see this language used extensively.
So the Temple and the Tabernacle are not a case of God changing his mind, but giving a way off understanding the greater event that is to come in Christ. Their role is to explain what happens in Jesus Christ. But when Christ's death happens, the Old Covenant is fulfilled, so aspects such as the Temple can pass away.
The issue you seem to be trying to address is that of 'progressive revelation'. It means that God tells Mankind what he wants him to know only a bit at a time. That's not because he wants to string him along, or lead him a dance. It's more about what Man can understand at any given time. It's the same line of reasoning that means we don't teach advanced physics to elementary school children - they won't understand it, and if you try to explain it they will get more confused than they were.
This is particularly tied to Romans 7, where Paul explains that the Law was given to man for a time. It was good that the law was there, and necessary at that time, but it wasn't God's final objective. The Tabernacle and the Temple were part of the journey towards where God wants Mankind to be. Saying that they were unnecessary would be like saying that there was no point in going to elementary school, because eventually you would leave elementary school and go to high school.