The idea of assimilation, especially in context of the U.S entails that even when you order a mixed vegetables soup, all you want to taste are the mushrooms.
The short answer to the question of why do many Indian immigrants in the U.S. do not assimilate with the dominant culture in America* is because of :
(1) certain inherent ideological problems in the idea of assimilation, and
(2) Indians engage into defensive structuring.
*(The question says non-Indians. Any stats on this? Who are designated as non-Indians?)
For detailed explanation and the long answer, see below.
Overall, Indians assimilate to the U.S. melting pot much less than other ethnic groups, with however a caveat: as far as economic assimilation is concerned, Indian immigrants are assimilated well.
Assimilation means a process in which a minority group/community integrates socially, culturally and/or politically into the the larger, dominant culture and society. The idea of assimilation does not mean that self-identification (as American) is the way to go. When the individual is accepted into the group, he or she has been assimilated or absorbed by the group.
In case of the U.S.A., there exists three dimensions in which an immigrant can assimilate: cultural, civic and economic.
Let's have a quick look on some data [1] and see what is going on in the U.S.A. The following figure shows an index of cultural assimilation to the U.S. by country of origin, from 2000 till the Gods went crazy....err...the recession hit.
In this graph, Cultural indicators mean marriage to a foreign-born spouse, the number of children in an adult’s household, the ability to speak English, and marital status. Indians have the lowest levels than any other immigrant group, as far as cultural assimilation is concerned. What the O.P. indicates in the question, points more to the cultural assimilation part, than any other form of assimilation.
Apart from Canadians, the other immigrant group that stands tall to being culturally assimilated in the U.S. are the Filipinos. So that basically means Canadians and Filipinos find it easy and are willing to make that assimilation to the overarchic American culture.
Now, let's have a look at the following figure.
In this graph, Economic indicators mean educational attainment, earnings, occupational prestige, employment status, and labor-force participation rates as compared to native-born Americans.
Except Mexico, El Salvador and Guatemala, almost all immigrant groups appear to be economically well integrated in the American nation.
Also note how both China and India rate high on economic assimilation levels, but rate lower in the cultural assimiliation levels, even lower than cultural assimilation index of El Salvador. Among these, Philippines stand tall in both the figures.
So what is going on here? Why are Indians willing to assimilate economically to the U.S., while refusing to budge on other dimensions of assimilation?
There are two points to in the answer to this question, delineating how assimilation could be a difficult process for certain minority groups like Indians:
1) Problems in the ideological level:
Everybody knows that socially there is quite a pressure to assimilate to that overarchic American identity, the official policy being the melting pot. Assimilation, or Americanization requires an anglification of all immigrants to an Anglo-Saxon culture, where heterogeneity in culture, traditions, identity and ethnic background all get to become a gooey soup, seasoned and set just right in accordance with a conservative Anglo-Saxon taste buds.
Note how the idea of the American is set to default not based on the the Aboriginals who are indigenous and original residents of America, since everybody else arrived in a boat in successive waves.
But the dominant culture or the default set point includes only the white, Anglo-Saxon part as the reference point and the model towards which everybody should blend themselves.
What, do you think, is the basis of primacy given to Anglo-Saxon subculture?
A related and very important question is, do immigrant groups vary in their abilities to blend with this Anglo-Saxon culture, as far as learning of discourses on behaviour, ethics, morality, religious tenets, cuisine, dress and such other factors are concerned?
Blending with something becomes difficult or easy based on not only the wish and agency (meaning of agency: a person or thing through which power is exerted or an end is achieved : instrumentality) of the people involved, but also on certain inherent characteristics of the minority group.
Assimilation is a complex process of taking things in and incorporating them as your own. It involves the movement of something through a permeable boundary. How permeable the boundaries are depends on perceptions by the immigrants themselves, perception of the minority group by the wider networks, as well as certain core philosophical ideas making up the ethnic identity of the minority group and the dominant group.
This is why a core idea of assimilation to the U.S., or Americanization--the theory of melting pot--has been criticized as unrealistic since it could not realistically hold true for all immigrant groups involved, based on the degree of difference from the dominant culture. The idea of melting pot also makes a reductionist assumption in that the Western Culture is demonstrated to be the culture to have in order to have a cohesive society.
It excludes the cultural heritage and lineage of non-European immigrants. It excludes people who were forcibly brought into the continent and made to go through a historical, cultural and ethnic erosion--The African Americans.
Ideologically speaking, the alternative to the melting pot policy has been suggested something akin to a salad bowl, where things are tossed and drizzled with some salad dressing, that is, one can appear being assimilated on the outside, but retain what they are on the inside.
The follow-up question has been directed towards having the need for a salad dressing: why have a dressing cover for all? And who gets to choose the dressing?
Anyway, since we are not supposed to ask uncomfortable questions to keep all the masters of the universe pleased and smiling, let's get to the second point.
2) Defensive structuring
The justification of having assimilation as a strategy for adapting in a multi-ethnic society is that homogenity leads to lesser tension in a society and leads to integration. To succeed economically and live well in a new society, assimilation is oftentimes a necessary precondition.
Even though Indian immigrants assimilate well economically, eyeballing the graph below will show that their overall levels of assimilation is below average, understandably because they do not well so much as far as cultural assimilation and civic assimilation is concerned.
Source: [2]
A basic premise of assimilation is that it is a time-taking process, and that there are significant generational differences in the process, within a specific ethnic minority. Indians are no exception. Second-generation Indians culturally assimilate better than first generation Indians.
However, as identified by the OP, first-generation Indians often exhibit what is known as defensive structuring (term coined by American Sociologist Bernard J. Siegel). Defensive structuring is often an adaptive strategy of choice by many immigrant groups, and involve the following:
1) Cultural Integration: Indians have certain key values that are deemed to be important for the cultural integrity of a group, such as the significance of the family, the supremacy of the parents, women being deemed as upholding the honour of the family, etc. If one thing topples over, it is supposed to send waves across and the whole structure is supposed to collapse like a house of cards.
A central feature of defensive groups is the subordination of the individual to the group. This is manifested in settling of disputes in an individual's life by authoritative entities who are deemed to be knowledgeable in the matter, generalization of co-operative effort in group activities (a wedding is decided by many people in the family), and emphasis on goal-oriented activities (need to do well in school so as to ensure "doing well" in life and that is the only purpose of studying).
The consequence is perceiving difference as a threat to one's culture. Therefore, little motivation is found for cultural assimilation.
2) Symbols and Identity: The values of an ethnic group are found in its symbols, which often serve as cornerstones of how we conceive of our identity. These could include language and special colloquialisms as well as particular ritualistic behaviour or customs. Following them is not a question of choice or is open to discussion. Alternative behaviour are carefully screened out.
In a foreign country where many of the Anglo-Saxon values appear as direct anti-thesis to Indian values (values on romantic love, difference in food preferences, outlook towards women, etc) symbolic imputations to identity become stronger in the new country. That is, an Indian living in India might not feel a threat to his culture or identity and choose to uphold the "being Indian" thing. But an Indian immigrant, under perceived threat of the erosion of his culture, might feel the need to buttress those symbols of his cultural/ethnic identity.
The consequence is social interaction and social participation only in Indian and South Asian networks or groups.
3) Communication and Interaction Patterns: In general, social intercourse with non-members are very limited in defensive societies like ours. When they are done, Indians tend to apply their conventional standards in those interactions (asking private questions, being repulsed by people who consume beef, hoping a woman wouldn't "expose" and if they do then slut-shaming her, tending to look down on lesser educated people, etc).
Indians also have very explicit rules of conduct, which are open to surveillance by elders in the community lest any discrepancy happens. Because cultural survival is perceived to be at stake, the cultivation of discipline becomes a prime goal of the elders/authorities. This means facing disapproval if you're dating that African-American or the White girl. And inter-marriage is an important dimension on how "cultural assimilation" is measured in the U.S.
In their social interaction in the U.S., not many Indians are willing to learn and find a common ground to interact with non-Indians such as Anglo-Saxon Americans (or Filipinos or African-Americans for that matter).
Acquaintances from very differently perceived ethnic group seldom become friends and part of weekend get-togethers.
This changes significantly in the second-generation.
Defensive Structuring does not interfere with economic assimilation or following the legal tenets of a country or enjoying equal rights. Therefore it is often the other alternative of choice to cultural assimilation, and is a mode of strategic response to survival in a new country.
Sources:
[1] Comparing Immigrant Assimilation in North America and Europe | Manhattan Institute
[2] Measuring Immigrant Assimilation in Post-Recession America