This article explains dwarven relations with the other races.
The Ironforge dwarves do not trust the Horde, as they've fought the orcs almost as long as the humans have. They accept the current truce, but chafe at the notion that they must stay away from the borders of Durotar. The titans left clues all over Kalimdor, and the Ironforge dwarves do not want border disputes to get in the way of their research. Some of the more adventurous dwarves refuse to abide by Jaina Proudmoore's command to stay away from Durotar, and explore the orcish homeland's outer regions anyways. They frequently have skirmishes with the jungle trolls who inhabit Durotar's borderlands.
Ironforge is the strongest nation of the Alliance, and the dwarves and humans are two of the most closely politically tied races in all Azeroth. The dwarves and humans have frequently formed political alliances, and both are founding member races of the Alliance. They both share a mistrust of elves.
They knew the work at Bael Modan (and other locations) would be noisy and disruptive to local inhabitants, but believed their search was of far greater importance than the comfort of the locals. It turned out that the digging up of Titan ruins appalls the tauren, an act they see as desecration of holy ground. The dwarves and gnomes suffer constant attacks from the Horde, especially nearby tauren from Mulgore. The tauren attempt to destroy Ironforge dwarf dig sites at every opportunity, hassling dwarven archaeologists any way they can and stopping just short of open warfare. The dwarves felt they had to drive a band of tauren out of the area who were proving to be such a nuisance. The centaur have also made forays against Bael Modan, but were repelled decisively each time. They believed these attacks to be from various rogue organizations.
The fact that we are dealing with various rogue elements out here leads me to believe we will need support from the King's Army. Not only will the excavation require military support, it would seem to my novice eye that the location of Bael Modan might be of strategic value to the Alliance considering the volatility of world politics in their current state.
Alas, I have digressed. There is much work to be done beneath the rock. I have spent too much time writing and not enough digging...
The most notable incident was the destruction of the Stonespire tribe's villiage in the Southern Barrens in the conflict between the two. Many tauren lost their lives or were forced off their ancestral lands during the ensuing battles. Gann Stonespire is one of the few remaining villagers and member of the tribe that was lost to the dwarves, who seeks vengeance against them, for the deaths of his brethren and continued destruction of his ancestral lands with explosives and destructive machines. The dwarves have also rejected attempts at diplomatic resolutions.
In addition to the Barrens dig-site, another outpost in Mulgore has outraged the local Bloodhoof tauren tribe, who believe the excavations are disrespectful to the Earthmother. The digging is enraging the kodos of Mulgore.This section concerns content exclusive to Cataclysm.
In Cataclysm, the dwarves refused to listen to the warnings of the tauren and angered the spirits of the Land they were violently excavating on with explosives. The infuriated Earth spirits killed the Bael'dun miners and the tauren now seek to calm them. 
Angry at the death of his son, a scout pilot and amatuer archaeologist , General Twinbraid mistakenly blames the goblins in Frazzlecraz mine due to finding the corpse of a goblin helper of Gann. General Twinbraid then orders the player to attack the goblin miners, telling the player to "Kill 'em All" and to "Lay waste to their whole grubby operation."  This attack likely did not help dwarf/goblin relations.
Lands of MysteryThis section concerns content exclusive to the Warcraft RPG, and thus unlikely to be canon.
Lands of Mystery had initialy described a more peaceful relationship. However Cataclysm paints a far different picture and makes no mention of any of the below.
While under constant threat of outsiders encroaching upon their ancestral lands, by both centaur and goblin, the tauren see little difference in the case of dwarves, despite a difference in motives. The tauren do not realize that the dwarves are searching for relics of their heritage, and not quick cash like the goblins. If they did they would likely allow the the dwarves to work in peace, and perhaps even with their blessing. The tauren respect the worship of of ancestors, and they would likely find the dwarves purpose similar enough to tolerate the digging, provided the dwarves also showed the proper respect for the land. Even though tauren and dwarves do not share good relations, they were eager to share knowledge of runes and titan myths.
After Brann Bronzebeard visited the dwarves of the Bael'dun Digsite he knew he needed to act before his friends were put in greater danger. While he visited Thunder Bluff he suggested to Cairne Bloodhoof that he send a group of his own people to work with the dwarves in exchange for making sure that the land was properly cared for. Cairne agreed to bring up his offer to his council of elders for discussion. Apparently it worked, as Baine Bloodhoof asked a group of young tauren to act as emissaries to the dwarven excavation of Bael’dun to convince the dwarves to cease their careless digging. Given enough effort, the tauren apparently convinced the dwarves to allow a shaman to oversee their site to make sure that the land is properly cared for during the excavation, and that the dwarves return to the land as much as they take.
- ^ Alliance & Horde Compendium, 57
- ^ a b Lands of Mystery, 40
- ^ a b Warcraft: The Roleplaying Game, 190
- ^ Lands of Mystery, 28
- ^ Alliance & Horde Compendium, 64
- ^ a b Khazgorm's Journal
- ^ http://cata.wowhead.com/quest=14491
- ^ http://cata.wowhead.com/quest=24631
- ^ http://cata.wowhead.com/quest=24632
- ^ http://cata.wowhead.com/quest=24747
- ^ http://cata.wowhead.com/quest=25104/digsite-status
- ^ http://cata.wowhead.com/quest=25182
- ^ Magic & Mayhem, 34