There’s no all encompassing answer that satisfactorily covers every instance and group of people that adopted Western clothing but I can riff off an old answer of mine about how Japan’s modes of dress was influenced and changed. The shift from Japanese traditional clothing to Western outfits being the mainstay of everyday wear should not be taken as a general answer that can be applied to all instances or groups of people.

With that disclaimer, let’s go!

Japan has a traditional type of clothing often generally referred to as ‘kimono’. And while it’s extremely common for most Japanese people to wear shirts, slacks, and jeans in their day to day life, many people still wear kimono.

In Japanese, 着物 kimono literally means 'thing you wear’. Now a days, when someone says kimono outside of Japan, it probably conjures up images of elaborate traditional dress and images of elegant women or high quality dress.

But everyday clothes were also called kimono. And kimono are not exclusively worn by women. The traditional clothes of Japanese men can also be called kimono. Pop media has contributed to the image of 'exotic' Asian women or geisha and the kimono has taken almost fetish like levels of sexual association by some people (in a similar way the china dress is). But in reality, while there are very showy examples of kimono, they are still quite normal clothing and it isn’t particularly surprising or strange to see modern Japanese people wearing it.

The first shift from kimono to western dress began with the Meiji Period during the mid 19th century, after the opening of Japan to foreign trade and influence. It was a part of the large importation of various technologies, knowledge & information, methods, foods, and various other things from the West.

A big proponent of adopting Western clothing was military dress.

The Japanese government were moving away from the old system of decentralized military power in favor of establishing a unified, government funded and nationally associated professional military in the style of Prussia or the British Empire.

In line with adopting the organization, doctrines, and equipment of these foreign militaries that they took inspiration from, the Japanese military leadership also decided that they would adopt their styles of dress and kit. Government decree forbid military men from wearing kimono to any official functions and/or while on active duty, forcibly committing a massive organization in Japan to adhere to the standards of Western dress. Government officials were also bound by similar rules put forth for the bureaucrats.

You can see here an illustration of what the average officers and line infantry would have looked like in the newly formed Japanese Imperial forces.

This was a time of many firsts for the Japanese military, including the first time they had a really unified command and a standardized uniform, uniting the armed forces of Japan in mind and body.

The other big driving force of adopting Western clothing were Japanese elites.

To see how rapid the changes made during the Meiji Restoration were, look no further than the Emperor himself. This is what Emperor Meiji looked like in the early days of 1872.

Later that year, he would cut off his top knot, a sign of hundreds of years of tradition, and adopt Western dress to symbolize his support for progress, pragmatic adoption of Western things, and a new Japan. This is what the Emperor looked like just one year.

The Meiji Restoration was a top-down movement to rapidly industrialize Japan and to make the transition smoother, the ruling elites of Japan believed that they needed to be able to absorb Western culture, language, science, and methods if they were to also be able to rapidly learn Western medicine, military strategies, economic systems, and earn a strong position in global politics. To be clear, they were not simply ‘trying to become Western’ or ‘become white.’

In fact, Japanese writers and leaders at the time were very explicit in wanting to take what they needed from foreign influences to become stronger and grow as a nation but were also intimately aware of the pressures it would put on their society and the dangers of Japanese values clashing with the influx of Western ideas as well as the inevitable changes it would have on the Japanese identity. At the same time, there was a exuberant curiosity in foreign, Western things and it was largely elites that led the way in searching out and consuming things that weren’t considered priorities by the Japanese leadership and government.

Western food, Western entertainment (to put the Meiji Restoration in context, Western composers like Wagner, Liszt, Brahms, Saint-Saëns, and Dvořák were all alive and making music during this time. Mozart and Beethoven had only been dead for aprox 20 years), Western literature, and of course, Western dress.

Most notably, men adopted suits rather quickly and it became the norm to wear a suit to work for the upper and middle class. Lower class citizens generally continued to wear their kimono, especially farmers. The tailored suit was not affordable nor necessarily easy to obtain for every member of society, even if one could obtain the money required. The Meiji Restoration affected urban populations the most, while rural areas generally just kept going about daily life as they always did.

Another notable thing is that women generally did NOT adopt Western dress. Many new ideas and ways of thinking were being born in Japan but increased gender equality was not one of them. Female participation in the labor market did not change a great deal during the Meiji Period and the majority of women remained the masters of the home and hearth. This meant that they still spent the greater part of their days at home, child rearing and maintaining the household.

Urban areas and certain industries were exceptions in that there were women that worked, owned property, etc. but this was a continuation of their situations from long before Western influences affected Japan.

Women quickly found that western dress was incredibly impractical for the inside of the average Japanese home. So the vast majority continued to wear kimono at home. As a matter of fact, most men also continued to wear the kimono at home as well. They would wake up, change into their suits, go to work, then come home and change into more comfortable kimono as home wear.

For elites, some women wore Western style dresses outside but many continued to wear kimono even outside. One of the big reasons was that for the first time, sumptuary laws from the Edo period that forbid the common people from wearing kimonos with silk or ostentatious colors, designs, etc. were repealed. The average Japanese women could now wear glamorous kimono that were previously only permitted on those of incredibly high status or even restricted to only the Imperial court.

It should also be noted that while kimono were still a large part of daily life in Japan, contemporary designs were also affected by Western dress. For example, the obi, the sash that is tied around the waist that holds the kimono together while also being decorative. Because of the repealing of sumptuary laws and a general change in the way society thought about clothes in public spaces, the way one could wear a kimono was relaxed quite a bit during the Meiji Period. For example, in this picture, the obi is tilted and simply tucked as opposed to being tied in a more complex and 'proper' way that would have been necessary for clothing etiquette during the Edo Period.

The obi was also featured lower and 'boxier’ than what was normally considered, as a result of the influence of Western dresses. With lower, boxier obi, the sillouhette of a woman's kimono now looked similar to that of a Western dress worn over a corset that accentuated the bust and hips into an S curve.

Out of room so continue below for the Taisho Period onward!

This answer is less why the vast majority of the world has adopted western style, and more about India and its unique mix of acceptance and rejection of it.

Unlike countries like Japan, Korea and China where, from a foreigner's perspective, traditional clothing seems relegated to holidays or religious functions, Indian clothing is as or even more widespread than western clothing in India. Western-style clothing would be a rare find in rural areas, and are more the purview of middle to upper class working professionals in urban centres.

The history of western clothing in India is undeniably tied to its history of colonialism. Colonial India's relationship with cloth and clothing (two different things, a division important to note when talking about the history of clothing in colonial india) was rooted in either the acceptance or rejection of Identity. 19th century Indians reacted in broadly three different ways to the introduction of British clothing:

1. Many upper class men started to incorporate certain elements of western style into their traditional dress. Examples would be the wealthy Parsi community where the men would typically combine baggy trousers (similar to harem pants), a long collar-less coat, formal boots and the phenta (hat). Apparently, walking sticks were also used as an accessory to complete the look of a gentleman.

Western clothes were a sign of modernity, of progress and, particularly to Dalit communities that converted to Christianity, freedom. Goan converts to Christianity started wearing trousers and coats. An important note is that most changes were limited to men, in the exception of certain cases like the case of the Nadar community in Kerala. The women in this community were typically barred from covering their upper bodies in the presence of the ruling Nair caste. Contact with Christian missionaries lead to the Nadar women covering themselves up -- a decision that sparked anger and riots in 1859 where the women were dragged into the marketplace and stripped and chapels were burned. The government then issued a statement that permitted Nadar women to cover themselves with a jacket, or in any manner they wished as long the style didn't copy the upper caste. Christianity and its association with western dress is something that continues to this day, where certain "Moral Studies" textbooks in Karnataka depict Indian Christians exclusively in western clothes -- contrasted with Hindus or Muslims in more traditional Indian styles.

2. There were many Indians who feared the cultural erosion that western clothing seem to promise. Nationalist thinkers mocked those who donned western-style suits. This can be seen in political cartoons of the late 19th and early 20th century. "The Modern Patriot" is a famous satirical picture by Gagenendranath Tagore that depicts a foolish and pot-bellied man who is adorned in western dress but claims to love his motherland. This was a common stock figure in many cartoons of that time.

3. Many men started wearing both Indian and Western styles -- a practice that continues in modern day India. Bengali bureaucrats stocked western-style clothing for work but changed into Indian clothes at home. Verrier Elwon notes policemen in 19th century Poona who would take off their trousers at the end of the day and walk home in "tunic and undergarments".

Western clothing was seen as a symbol of British rule. Attempts to cement this perception lead to an 1830 ruling that forbade Europeans from wearing Indian clothing at official functions. Wealthy Indians would continue to include western styles into their wardrobe -- the three piece suit was particularly favoured -- but always maintaining certain symbols of their country. An example of this would be leading officials and technocrats in Mysore who would frequently combine the Mysore Turban with a three-piece suit -- a sign of belonging to a princely state and a symbol of the dual identity that came with being under British rule but also having semi-autonomous control of your land.

Positive associations with western clothing were increasingly challenged in the twentieth century. The Swadeshi movement is a hallmark of anti-British sentiment. A movement that explicitly encouraged Indians to boycott British goods and start their own industries. A famous image that captures the heart of the movement is that of Mahatma Gandhi, bare chested, sitting with his spinning wheel. Gandhi sought to spread the use of Khadi (a coarse cloth that was seen as more patriotic than the British mill-made cloth), and this view was repeated in many poems and songs of that time. (This is where the difference between cloth and clothing comes in, by the way).

However, the change of dress appealed mainly to those of upper castes who could afford Khadi -- which was more expensive and harder to find than British textile imports. Gandhi's dream to clothe the entire nation in Khadi could not compete with cheap British goods. Even nationalists like Nehru who wore the Dhoti and Kurta did not wear ones made of coarse cloth.

Additionally, the connection between western dress styles and freedom from caste norms was never severed to Dalit nationalists like Ambedhkar, who never gave up the western style suit.

Combine this with post-colonial globalisation and increasing proliferation of American media and fashion among urban youth, the dream of Khadi is dead. This isn't to say, however, that India has largely accepted western-style clothing. The dhoti and Kurta remain formally accepted forms of dress and are frequently donned by politicians. The Saree and the Salwar Khameez enjoy immense popularity among Indian women -- even in professional urban centres. A good example would be the pictures of the female scientists who helped send a satellite into space: all clad in sarees, all still regarded as professionals. Additionally, the use of sarees seem to be an unwritten rule for many female politicians to an extent where even Sonia Gandhi (a foreign-born politician) almost exclusively dons them. It's both a symbol of solidarity with the ordinary Indian woman and an observation of grander patriotic sentiments that see traditional clothing as a symbol of "being a true Indian". The youth in both urban and rural areas increasingly wear western clothing, as prices of western clothing continue to fall and become more accessible. Additionally as gender equality rises in the workplace, women feel less pressure to only wear Indian clothing, and it's a common sight to see Indian girls in jeans and a shirt. It's an affirmation of affluence but also freedom -- quite like 19th century Indian men in that regard.