As some readers accurately pointed out, there are much bigger injustices occurring at the Temple Mount. While I chose to focus on the internal issue, as its generally better to focus on internal improvement rather than outside castigation, I've decided that the points raised by several readers deserve to be heard as well.
And now, onto the substance. Jews tend to focus on the Kotel, the Western or Wailing Wall. In fact, when one visits the Kotel, it's not uncommon to see Jews kissing the wall, placing notes containing prayers in the cracks of the wall, and other such gestures of veneration. The prayers of the world's Jews are directed towards Kotel, or so many think. In reality, our prayers are directed (or supposed to be directed) towards the location of the Kodesh HaKodashim, the Holy of Holies, which was located somewhere near the center of the Temple Mount, and represented the resting place for no less than God's presence on Earth. Many decisors of Jewish law are actually of the opinion that someone who prays at the Kotel should direct their prayers towards the center of the mount (on an angle to the left of the wall) rather than at the wall, as is the common custom. All of this to say that we've mistakenly elevated the value of the Western Wall in our mind above the immensely significant heritage of our two past Temples and the true import of the site.
Now, on the Temple Mount itself. The Dome of the Rock (constructed as a political monument in the year 692 c.e.) rests on the most important spot in the national and religious heritage of Israel and the Jewish people. In addition, the comparatively smaller and more recent Al-Aqsa mosque sits oblique to the Dome as a place of Muslim and only Muslim prayer.
Though there are many complaints one could fairly lodge (such as truth about the actual importance of the site in Muslim theology and history), I'll focus on the main one. Though Jews and other non-Muslims can tour the Temple Mount under the close watch of Israeli authorities at designated times, they cannot pray there. This is strictly enforced by the Israeli authorities, as part of an agreement they voluntarily entered into with the WAQF, the Muslim authorities who control the site. When tour groups go up, they watch closely to make sure no one talks or so much as dares to pray or do something that would offend the Muslims. This is true not just for Jews but for all non-Muslims. Imagine, for a moment, all non-Jews being banned from Jewish holy places, and a unit of armed officers watching closely to enforce the ban. We would never do such a thing, as we believe that our God is the only God, and therefore everyone's. He cares about all people, and desires their heartfelt prayer. In fact, we earnestly pray for the day when all nations will come to our Temple to pray to the one God. "[M]y house shall be called a house of prayer for all peoples" (Isiah 56:7). It's with this thought that we conclude prayers on Yom HaKippurim and other holy days, representing our sublime yearning for unity in the face of our human condition and the existence of one omnibenevolent God.
As Abraham Joshua Heschel eloquently stated at a 1963 conference on race and religion, "What is an idol? Any god who is mine but not yours, any god concerned with me but not with you, is an idol."
The Islamic rule stands in sharp and shocking contrast. This highlights an important general point about religion. Some faiths use religion and God generally as ideas to belittle others and promote themselves. This is the creed of many outside of our faith, and though it is not our creed, manifests itself too often within the Jewish community. True faith enhances all of our lives and allows us to work together.
Now, the thought that Israeli authorities would enforce such a blatantly racist and unfair agreement on behalf of the Muslim authorities is quite disturbing in its own right, and seems to represent the worst violation of the the Rabbinic idea that one should not sin, nor aide in the commission of one. The Israelis are guilty as accomplices. That we can actively enforce a ban on prayer for all non-Muslims is a violation of the most basic ideals of the Jewish faith, yet also of western democractic ideals.
Unless the issue is brought to light and people make their voices heard, the status-quo will remain. Frankly, Muslims will make more noise and will be more upset about a change to the current standard than Jews and others are currently, and so they will continue to "win" for fear of the consequences. It's long past time Israel made some fairness one of its mainstream political demands, and certainly time for Jews, believers in God, and others who value democracy to make their voices heard.