It has become a common belief that all Icelanders believe in elves and other supernatural beings often called "Huldufólk".

It has become a common belief that all Icelanders believe in elves and other supernatural beings. While that may not necessarily be completely true, it definitely holds some truth about their influence in Icelandic culture. In fact, there have been occasions in which major decisions were made with the elves in mind. 
The rise of the ‘Elf Lobby’
In the 1930´s, the government was trying to connect the outlying town of Kópavogur with the capital of Reykjavík. However, road construction crews continuously ran into trouble because of Álfhóll, a sizeable rock known as Elf-hill. The rock sat right in the midst of the planned route and had to be either broken or removed to continue, something the construction crew decided not to deal with at the time. A decade later, construction equipment was continuously broken or lost, leaving crews to abandon the project once again. In the 1980´s, the rock drew media attention and public support. Today, the road passes around Álfhóll, leaving it untouched.
Protecting Elves, Protecting Nature 
According to a New York Times article published in 1982, Icelanders protested the North Atlantic Treaty Organization (NATO) on the grounds that a military establishment in Iceland would harm the elf population. As Iceland was a strategic location for monitoring Soviet activities during the Cold War, the U.S. stationed troops and military equipment in Keflavík. The presence of the base was not welcomed by Icelanders in general, and those who protested were foremost against anything that would bring destruction to the environment. In this way, belief in Elves has become akin to environmental stewardship; what is bad for the environment is also bad for the Elves. 
Where Does the Myth Come From?
The origin myth of the hidden people, or Huldufólk, goes that one day God decided to pay a surprise visit to Adam and Eve. However, Eve did not have time to wash all of her children and didn’t want God to see the unclean ones, so she hid them away. When God asked if all her children were present, she lied, and as punishment God made it so that the hidden children would be hidden from the world forever. 
These Huldufólk made their homes in the landscape. If this sounds like a mix of many familiar stories, it is just that. The first settlers in Iceland in the 10th century were a mix of Irish slaves and Norwegians who brought their own folklore and mythology to Iceland which continued to exist alongside Christianity as it became the dominant religion. 
Other stories maintain that men have fallen for Elvin women and followed them to their homes, emerging years later thinking they had only been gone a few hours. Reportedly, they are very similar to humans in size and mannerism and curiously clad themselves in 17th century clothing. Hafnarfjörður, a town just outside of Reykjavik, is reportedly the seat of the Elf kingdom in Iceland and has the highest population of Elves. In this harbor town it is possible to take a guided Hidden People walking tour of the city that explores folktales and other sites related to this phenomenon. 
It seems that Icelanders maintain a certain respect for huldufólk. Most Icelanders denied the existence of huldufólk when asked directly, but when they were then given a hammer and asked to smash an ‘elf rock’, almost all refused to do it.