Temples are holy places.
Footwears have dirt on them which could make the temple floor dirty.
Hence, as a respect towards God's place, people leave their footwear outside.
Even people should be clean when entering a temple; for example, in some places, people gargle with water if they have eaten something a few hours before visiting the temple.
Also, this is not just applicable to temples, but this is also a common practice amonst people not wearing footwear in their homes.
Usually, Temple authorities display a board which says "Footwears are strictly prohibited" as our temples can be visited by people of other religions who may not be aware/care of this respect shown by Hindus.
hinduism.stackexchange.com/users/93/Mr_Green
To clarify some more things (rightly pointed out by Mr_Green), we CAN take footwear inside a temple.
The footwear allowed inside a temple is called Khadau .
It is purposely used by priests, and those who work inside the temple.
A Khadau is essentially the old style footwear.
It is made of wood.
Modern day footwear are not considered holy as these are.
We now make footwear with things mostly prohibited to take in use.
They also get dirty soon enough.
There is perhaps, more to this.
Wooden footwear keep the mind cool and are insulators of electricity and heat (wood used to make footwear doesn't catch fire!).
So, footwear is allowed in temples, but not "modern footwear" , due to the above stated reasons...
hinduism.stackexchange.com/users/75/user3459110
Since no answer gives any reference from any scriptures, i am adding my own.
The reason is scriptural injunction .
That is, scriptures ask us not to wear shoes where idols are placed.
There are 5 such places where one is prohibited to enter with shoes on.
They are: The room where the Vedic fire has been established.
2.
A cowpen; Goshala or where the cows stay.
3.
A place where a Deity is installed, like a temple or a Puja room and a room for the Brahmin.
4.
A place for taking meals.
5.
The room where one chants the Gayatri.
One should leave off his shoes [before entering] the house in which the Sacred Fire is deposited, a cow-pen and the presence of a Deity, or a Brahmana, [and before] taking his meals, or reciting [the Gayatri].
(61)
[If a person] putting on [his] sandals, goes, from his house, to the Five Rooms,* a pious king should cut off his two legs.
(62) Angiras Smriti 1.62,63.
However, these rules do not apply for the following special persons:
An Agnihotrin (i.e., who maintains the Sacred Fires), an ascetic, a S'rotriya, one who has completely-studied the Vedas ; these may go there with [their] sandals on ; others must be chastised with punishment.
(63) NOTE:
Angirasa Smriti is counted among the 18 major Smritis that we have.
hinduism.stackexchange.com/users/4732/Rickross
Generally footwear is made up of leather.
In the Hindu religion they are considered to be an impure thing.
One more thing is that the temple is a holy place where everyone worship.
And footwear also consists of outer dirt as Mr_Green has mentioned in his answer .
So we can't take those dirty shoes inside that holy place.
In temples not only footwear needs to be removed.
The upper cloth, that is, your shirt and t-shirt also need to be removed as for worship with Dhoti.
hinduism.stackexchange.com/users/130/The Hungry Dictator
Shoes are not clean since they go everywhere.
Since a temple is a clean place with pure energies, we leave unclean things outside.
Detailed Answer:
There are a few views offered on this subject.
Shoes go everywhere and can collect unwanted energies.
To keep them out of the temple shoes are left outside.
Second, generally temple practices encourage minimum amount of covering, subject to what would be considered decent in the respective social setting.
This may be related to the ability for energy interchange – the temple being a highly energized place.
In that context, among various parts of the body, the soles of the feet are considered points of significant interchange of energy.
This way when one walks in the temple bare foot, the interchange of energy gives the bliss and high of being in the temple.
While the two views noted above are the popular reasons for not wearing footwear inside the temple, there are some additional observations worth noting with regard to footwear use in temples.
There are certain temples in northern India that allow wooden Paadukas to be worn during winter months.
In fact, the temple itself provides the wooden Paadukas for a small fee, essentially ensuring that the footwear that goes everywhere outside the temple does not come into the temple.
In Udupi Krishna temple, the eight Acharyas only [not devotees] are allowed wooden Paadukas anywhere in the temple premises except in the shrine area itself.
Morden footwear is made out of leather mostly, leather comes from a cow!
Hindus & tamils are not allowed to eat beef.
We worship a cow as a mother because a cow gives us milk & its a holy animal.we are not allowed to eat pork because its the filthiest animal but most hindus/tamils still eat it, its not as bad as eating beef.
So you cannot wear anything leather in most temples or go close to anyone with trans wearing leather.
Shoes are forbidden because we not allowed to take the dirt into the temple.
hinduism.stackexchange.com/users/2347/Tia Budram
According to books I have read ancient foot wares were made of animal skin and therefore killing of animals is not accepted by our religion .So
in order to ban these foot wares temple authorities implemented this rule,so from the ancient times the foot wares was prohibited in temple
and it is being followed till the present day
hinduism.stackexchange.com/users/14752/Akash. B
Footwear irrespective of it being made from leather/rubber etc has to be removed mainly because of dirt that comes along...
most temples even in Europe/
North America also have feet washing facilities at the temple entrance.
That said, Even Hindu temples in North america does not allow shoes inside inspite of cold weather,but you are allowed to wear socks P.S:
Most Indians (irrespective of religion) remove footwear before entering a house to keep their home clean.
hinduism.stackexchange.com/users/246/QuickBlue
Why is it that people don't wear shoes and sandals when they visit a temple? Sometimes they remove them outside of temple premises and sometimes outside of the temple steps...  It's a common practice amongst Hindu people whenever they visit a dharmik sthal/temple, so what's the reason behind removing footwear outside?  And is there a rule to do so, or do people just follow a common norm?   Credits for the image:  double-barrelledtravel.com
Why do Hindus remove their footwear before entering temples?
hinduism.stackexchange.com
<worship><temple>
hinduism.stackexchange.com/questions/639
hinduism.stackexchange.com/users/124/Mr. Alien
Footwear irrespective of it being made from leather/rubber etc has to be removed mainly because of dirt that comes along. One should leave off his shoes [before entering] the house in which  the Sacred Fire is deposited, a cow-pen and the presence of a Deity,  or a Brahmana, [and before] taking his meals, or reciting [the  Gayatri]. Shoes are not permitted inside temples so as not to bring dirt into the temple. A temple is a clean place, with pure energies, so unclean things are left outside. Shoes go everywhere and can pick up unwanted energies.
Shoes are not permitted inside temples so as not to bring dirt into the temple. A temple is a clean place, with pure energies, so unclean things are left outside. Shoes go everywhere and can pick up unwanted energies. The scriptures ask us not to wear shoes where idols are placed. People should remove their shoes before entering a place with a Sacred Fire, a cow-pen, a presence of a deity or a Brahmana, before taking meals or reciting the Gayathri. The scriptures ask us not to wear shoes where idols are placed. People should remove their shoes before entering a place with a Sacred Fire, a cow-pen, a presence of a deity or a Brahmana, before taking meals or reciting the Gayathri.