An Unholy Tribulation Temple?

Is the future Tribulation Temple unholy? On a fairly regular basis, I see comments by futuristic premillennialists of all stripes calling the tribulation temple "unholy" or even a "fake" temple.

Incidentally, I regularly spot "fake modern Israel" tags from some premils. These folk observe that modern Israel is in a state of unbelief. They'll cite Paul's comments regarding what constitutes a true Jew (true Israel). The same folk do it regularly enough that I suspect in some cases there's an underlying animus driving it. But that's another story for a future axe to grind.

Is the future tribulation temple unholy? What does Scripture say?

Therefore when you see the abomination of desolation which was spoken of through Daniel the prophet, standing in the holy place (let the reader understand), then let those who are in Judea flee to the mountains Matt 24:15-16 (see also Dan 9:27; 11:31; 12:11)

....who opposes and exalts himself above every so-called god or object of worship, so that he takes his seat in the temple of God, displaying himself as being God.  2 Thess 2:4

Given the above verses, how can an Abomination of Desolation occur in a fake temple? How can something unholy stand in a holy place, in a fake temple? Can the temple of God be a fake temple? Can a fake temple be desecrated?

I infer from certain verses that unbelieving Israel will be brought to final salvation through a process. This will occur during a future tribulation. Perhaps the temple is a marker of that process.

BUT, please note that I'm not claiming the 70th week sacrifices in a tribulation temple contribute to Israel's salvation. Salvation is always by grace through faith in Christ.

More on the process...

I will return again to My place till they acknowledge their offense. Then they will seek My face; In their affliction they will earnestly seek Me. Hos 5:15

….so that they will look on Me whom they have pierced; and they will mourn for Him, as one mourns for an only son, and they will weep bitterly over Him like the bitter weeping over a firstborn. Zech 12:10

O Jerusalem, Jerusalem, the one who kills the prophets and stones those who are sent to her! How often I wanted to gather your children together, as a hen gathers her chicks under her wings, but you were not willing! See! Your house is left to you desolate; for I say to you, you shall see Me no more till you say,`Blessed is He who comes in the name of the LORD! Matt 23:37-39

Then the sign of the Son of Man will appear in heaven, and then all the tribes of the earth will mourn, Mat 24:30

What do you think?

For more on this topic see Randall Price's book "The Temple and Bible Prophecy." Chapter 23 "Blasphemy or Blessing - Sacrifices in the Last Days Temple" is helpful. See also his website and this article.