They do not believe in the true God because, as Jesus said multiple times, anyone who rejects Him also rejects God the Father. No future physical temple would ever be ordained to be built by God, so no future physical temple is a temple that scripture would call God's temple or the temple of God. Nowhere in scripture does it describe a future fake temple of God being built as part of the fulfillment of any prophecy.
I disagree with your claims made, Isaiah 66:1-4 strongly suggest that a 3rd temple will be built and animal sacrifice resumed, yes it will be an abomination to the Lord and the Cross of Calvary
When the Jews build in the future they will be building to the Hebrew "God" of the Bible, not some foreign god like, Buddah, Shiva, Etc
The key is you clearly see the renewed animal sacrifice taking place in this house/temple being built for God, verse 3 and God is showing his disapproval
Isaiah 66:1-4 strongly suggest a rebuilt house/temple dedicated to God by the Jews, with renewed animal sacrifice, this will be an "Abomonation" to the Lord and the cross of Calvary, God will send them a strong delusion
Point Of Interest: The word "Delusion" is used 2 times in the KJV, and they are both associated with a house/temple, and it appears that the scripture presented could be "Parallel Readings" of the same event?
Isaiah 66:1-4KJV
1 Thus saith the Lord, The heaven is my throne, and the earth is my footstool:
where is the house that ye build unto me? and where is the place of my rest?
2 For all those things hath mine hand made, and all those things have been, saith the Lord: but to this man will I look, even to him that is poor and of a contrite spirit, and trembleth at my word.
3
He that killeth an ox is as if he slew a man; he that sacrificeth a lamb, as if he cut off a dog's neck; he that offereth an oblation, as if he offered swine's blood; he that burneth incense, as if he blessed an idol. Yea, they have chosen their own ways, and their soul delighteth in
their abominations.
4
I also will choose their delusions, and will bring their fears upon them; because when I called, none did answer; when I spake, they did not hear: but they did evil before mine eyes, and chose that in which I delighted not.
2 Thessalonians 2:10-11KJV
10 And with all deceivableness of unrighteousness in them that perish; because they received not the love of the truth, that they might be saved.
11 And for this cause
God shall send them strong delusion, that they should believe a lie: