People also tend to play games with the halachic aspects of it.
But Rav Avigdor Miller clarifies it down the nitty-gritty in the following Q&A.
Basically, the Temple Mount obviously belongs to Am Yisrael.
No doubts, no questions.
(Just false claims from other religions.)
But we aren't allowed to go there due to our lack of purity with no way to purify as in days of yore.
But it IS ours!
And not only are we not allowed to go there, but NO ONE is allowed to go there.
It's simply too holy.
Here is Rav Avigdor Miller from December, 2000:
Rav Avigdor Miller on The Temple Mount: Who Does It Belong To?
In light of what Prime Minister Sharon has done recently by going up to Har Habayis in order to show a modicum of Jewish sovereignty there, would you say that the Har Habayis better off in Jewish hands or is it better off in Muslim hands?
I’m going to tell you a little anecdote first.
When I first wrote my book Rejoice O Youth, I had no money to print it. I needed two thousand dollars; I didn’t have the two thousand dollars.
So I went to Mr. Feldheim, alav hashalom; I thought maybe he’d take my manuscript.
I showed it to him and he opened it up just at that place where it says how good it is that the Mohammedans have the Har Habayis because if Jews had it, then the women would come there with their shorts and they’d profane the place.
But now that the gentiles are there, Jews can’t profane the place.
(In Rejoice O Youth on page 146, paragraph 272, Rav Miller writes: “The Mohammedans protect the holy ground [of Har Habayis] not only against idol worshippers and against images, but also against irreverent Jews. If the Jews could have access to the holy place, they would come with their women and cameras and their lunches and desecrate the holy grounds. Besides we are all unclean today, so it will be a great sin for Jews to ascend the mountain of the Holy House.”)
He saw that and he looked at me. “I don’t know if the book will sell,” he said. People don’t like to hear that.
Now let me say something.
We don’t want the Mohammedans to have jurisdiction there. We are the ones who own the place and we can tell them that.
However, we don’t want Jews to go there at all. Chas v’shalom! It’s kareis to go there today. We’re temei meisim. We can’t go there.
And if we would permit Jews to go there, you could be sure there would be picnicking there and there would be all kinds of tumos and nevalos there. That’s out!
And therefore, we’re better off that no Jews can come there. That’s the truth!
Of course, we should say we have the right to own that land and therefore you have no right to dig in there and to break up any artifacts you find.
No. That we can demand.
And we can punish them in court for doing those things. שועלים הלכו בו – Foxes walk on that place. They’re foxes, it’s true.
But Jews can’t go there anyhow. That’s all.
TAPE # E-259 (December 2000)
(Used with permission from https://torasavigdor.org/)