On shrines, most of them are the tombs of Muslims saints, typically sufis. (Sufi means "mystic", incidentally). Revering local holy men was a sufi tradition, and a way they made "syncretic" compromising with pre-Islamic religious traditions. Somewhat similar to the cult of saints in Catholicism, at least in some cases.
Purist Muslims and literalists in particular have a rather dim view of the cult of saints. It was a grass roots thing at the periphery of Islam. Ibn Tayymia in particular was an opponent of it, considered it a form of idolatry and what they called "associationism" - associating other figures with God, which they regarded as a heresy of the Christians in particular. Tayymia was an opposition figure in his own day, and it was his hatred of the cult of saints that got him thrown in jail for heresy. He objected to the ritual in the regular pilgrimage to Mecca that had the pilgrims pay their respects at Muhammad's tomb.
The Wahhabis took from Tayymia a loathing for the cult of saints in any form. The only allowed place of worship is a mosque, which must be devoid of any representational art (as idolatry - that is why they are all periodic tiles, no pictures - the only other allowed "decoration" is calligraphy, verses from the Koran written out in Arabic). This is not all that popular with sufi Muslims, but these days they tend to get their way.
They dislike the idea of any form of worship going on anywhere in which anything or anyone is associated with the worship, or with God, or is represented. This is not restricted to their own, but extends to anybody else's worship, too. Idolatry should just be stamped out wherever it exists, that is the belief of the Tayymia style literalists. Take over any pagan temple, cleanse it of images, make it a mosque - sure that is something they did a lot of in places they ruled.
As for the temple mount it is certainly a special case, as is the kabba in Mecca. Mecca was a pagan religious center in Muhammad's day, with hundreds of idols worshipped there, including the stone. He threw the pagans out and made it a center of Muslim worship. Before going to Medina, he had prayed toward Jerusalem. While in Medina he came into violent conflict with the Jews there, and changed the direction of prayer, toward Mecca.
Muhammad thought of himself initially as continuing a revelation first made to the Jews. He thought the religion of Abraham was the true religion and that he was bringing it to the pagans of Arabia. That Judaism as distinct from the religion of Abraham was a later development of it, that (he thought) had become encrusted with particular human additions related to one people, instead of being a monotheism addressed to all, as he took Abraham's religion to be.
He expected praise from the Jews who he initially thought of as a particularly pious people compared to the pagan Arabs around him. When instead they considered him a heretic he took offense, developed a strong dislike for the Jews he met in Medina, and persecuted them ruthlessly. The official line is that the Jews were given a true revelation but messed it up, interpreting it too particularly as making them special, yada yada. As for Christianity, Islam treats Jesus as a saint but a man, distorted by his followers who commit polytheism by associating a lesser figure with God.
All of which means Jerusalem is of course still extremely important to Muslims. But since Islam's take on them is less than charitable, they think they should be in charge of all the holy sites, and that the others' use of them contains impiety etc. In the late 7th and early 8th centuries the Muslim structures there were built, and all sorts of stories about the supposed importance of the sites were laid down. The dome of the rock is supposed to be the location of Muhammad's "night journey". But it was clearly meant as a challenge to Christians, and contains inscriptions exhorting Christians to forswear the idea of God having a Son and to worship only one God instead. Obviously it is also on the site of the former Jewish temple, destroyed by the Romans centuries earlier. The location of the al-Aqsa mosque is supposed to be the site of Abraham's near sacrifice of Isaac, a reference clearly meant to underscore Islam's claim to be descended from the religion of Abraham, with little historical basis.
So there is an element here that is clearly just aggressive, your religion is wrong, ours is right, the right one should be followed everywhere, especially in the places you think are important to be in your face about it and continually draw attention to our belief that you are wrong, etc. The same motive is doubtless also at work in things like fights over shrine locations in India. But there, there are two other motives. One, there are some sufis who actually care about their particular shrines in a religious sense. Two, there are other fundamentalists who hate that any so-called Muslims care about shrines, and about the too-religious sense they do care about them, and would rather they didn't. To the point of wanting them pulled down, in some cases.
I hope this clarifies things a bit. Please understand I am giving information here about what they think, not endorsing a line of it. Particularly the literalists, there is no reasoning with them, their minds are completely shut off. That isn't so with the less irrationalist of the sufis, with the more moderate of the Shia, with modernizers (thin on the ground but not zero), and even with traditionalist opponents of Tayymia style bigotry. Ghazali isn't Tayymia, Fazlur Rahman is not Sayyid Qutb. People who read and think like the first in each pair you could reason with; the second two, forget it.
Required reading. Thank you so much for your knowledge and insight. My hope is that the rest of the world, whether Christian or otherwise will wake up. Of course for me, it's all in God's plan.
Required reading. Thank you so much for your knowledge and insight. My hope is that the rest of the world, whether Christian or otherwise will wake up. Of course for me, it's all in God's plan.