Short answer
No. Most of the values people mean by Western are honesty, hard work, care for family, charity, keeping the law and being a good neighbour. Islam commands every one of them, often more strictly than the law does. A Muslim must keep his contracts and give a fixed share of his wealth to the poor. He must keep the laws of the country that protects him. The Prophet (ﷺ) said the angel Gabriel urged kindness to neighbours so often that he thought neighbours would inherit. In daily life the differences are few: alcohol, sex outside marriage, interest and dress. On these the West itself once stood close to Islam. The Church forbade interest for centuries, and America banned the sale of alcohol in 1920. Muslims simply did not change when the West did: they keep the standard God (﷾) gave them, and it does not change with fashion.
Full explanation
The values Islam already commands
The Qur'an defines righteousness as faith put into action. That means giving to relatives, orphans and the poor, regular charity, and keeping the contracts one has made. It commands kindness to parents in their old age, and to neighbours near and far. The Prophet (ﷺ) said the angel Gabriel pressed him so often about neighbours that he thought they would be made heirs. So the family next door gets a neighbour who does not drink or gamble, and who looks after his parents at home.
“It is not righteousness that ye turn your faces Towards east or West; but it is righteousness- to believe in Allah and the Last Day, and the Angels, and the Book, and the Messengers; to spend of your substance, out of love for Him, for your kin, for orphans, for the needy, for the wayfarer, for those who ask, and for the ransom of slaves; to be steadfast in prayer, and practice regular charity; to fulfil the contracts which ye have made; and to be firm and patient, in pain (or suffering) and adversity, and throughout all periods of panic. Such are the people of truth, the Allah-fearing.”
“Thy Lord hath decreed that ye worship none but Him, and that ye be kind to parents. Whether one or both of them attain old age in thy life, say not to them a word of contempt, nor repel them, but address them in terms of honour. And, out of kindness, lower to them the wing of humility, and say: "My Lord! bestow on them thy Mercy even as they cherished me in childhood."”
“Serve Allah, and join not any partners with Him; and do good- to parents, kinsfolk, orphans, those in need, neighbours who are near, neighbours who are strangers, the companion by your side, the wayfarer (ye meet), and what your right hands possess: For Allah loveth not the arrogant, the vainglorious;-”
Aisha reports that the Prophet (ﷺ) said the angel Gabriel kept urging him to treat neighbours well, so often that he thought Gabriel would make neighbours heirs.
Keeping the law of the land
The Qur'an binds a believer to every agreement he makes. Muslim scholars hold that living under a country's protection is such an agreement. This is true whether he lives there by birth, settlement or visa. The Prophet (ﷺ) told Muslims to obey those in authority, whether they like it or not. The one exception is an order to sin. In the West that exception almost never arises. The law allows drink, gambling and sex outside marriage, but it commands none of them. Nor may any private Muslim, in the West or anywhere else, punish anyone under Islamic law. Those penalties belong only to the lawful ruler of a Muslim state or the judge he appoints. A Muslim who refuses a drink breaks no law.
“O ye who believe! fulfil (all) obligations.”
“Come not nigh to the orphan's property except to improve it, until he attains the age of full strength; and fulfil (every) engagement, for (every) engagement will be enquired into (on the Day of Reckoning).”
Abdullah ibn Umar reports that the Prophet (ﷺ) said a Muslim must listen and obey those in authority, whether he likes it or not, unless he is ordered to disobey God. If he is ordered to commit a sin, there is no listening and no obeying.
Ibn Qudamah, a Hanbali jurist, holds that, as a rule, no one may carry out a fixed penalty (hadd) except the ruler (imam) or the one he appoints to act for him. The only exception he allows is an old ruling on a master and his own slave, which has no application today.
Respect for people of other faiths
The Qur'an says there is no compulsion in religion. It allows Muslims to deal kindly and justly with people of other faiths who do not fight them or drive them from their homes. So a Muslim is told by his own scripture to be fair to the neighbour who does not share his faith.
“Let there be no compulsion in religion: Truth stands out clear from Error: whoever rejects evil and believes in Allah hath grasped the most trustworthy hand-hold, that never breaks. And Allah heareth and knoweth all things.”
“Allah forbids you not, with regard to those who fight you not for (your) Faith nor drive you out of your homes, from dealing kindly and justly with them: for Allah loveth those who are just.”
Where Muslims do differ
In everyday life the differences are few. The Qur'an forbids intoxicants, such as alcohol, and gambling. It forbids sex outside marriage and lending at interest. It tells men and women alike to lower their gaze and guard their modesty. These are the points where a Muslim will not follow the fashion around him.
“O ye who believe! Intoxicants and gambling, (dedication of) stones, and (divination by) arrows, are an abomination,- of Satan's handwork: eschew such (abomination), that ye may prosper.”
“Nor come nigh to adultery: for it is a shameful (deed) and an evil, opening the road (to other evils).”
“Those who devour usury will not stand except as stand one whom the Evil one by his touch Hath driven to madness. That is because they say: "Trade is like usury," but Allah hath permitted trade and forbidden usury. Those who after receiving direction from their Lord, desist, shall be pardoned for the past; their case is for Allah (to judge); but those who repeat (The offence) are companions of the Fire: They will abide therein (for ever).”
“Say to the believing men that they should lower their gaze and guard their modesty: that will make for greater purity for them: And Allah is well acquainted with all that they do.”
“And say to the believing women that they should lower their gaze and guard their modesty; that they should not display their beauty and ornaments except what (must ordinarily) appear thereof; that they should draw their veils over their bosoms and not display their beauty except to their husbands, their fathers, their husband's fathers, their sons, their husbands' sons, their brothers or their brothers' sons, or their sisters' sons, or their women, or the slaves whom their right hands possess, or male servants free of physical needs, or small children who have no sense of the shame of sex; and that they should not strike their feet in order to draw attention to their hidden ornaments. And O ye Believers! turn ye all together towards Allah, that ye may attain Bliss.”
The West once stood close to Islam
None of these is an ancient Western value that Muslims refuse. The Bible forbids charging interest to the poor. In 1312 a Church council, the Council of Vienne, dealt with usury (lending money at interest). It ruled that anyone who stubbornly said usury is not a sin should be punished as a heretic. The New Testament tells believers to flee fornication (sex outside marriage) and tells women to dress modestly. Western manners held to this into the twentieth century. The United States banned the making and sale of alcohol by an amendment to its Constitution that came into force in 1920. What changed was the West.
“If thou lend money to any of my people that is poor by thee, thou shalt not be to him as an usurer, neither shalt thou lay upon him usury.”
The council decrees that anyone who obstinately maintains that practising usury is not a sin is to be punished as a heretic.
“Flee fornication. Every sin that a man doeth is without the body; but he that committeth fornication sinneth against his own body.”
“In like manner also, that women adorn themselves in modest apparel, with shamefacedness and sobriety; not with broided hair, or gold, or pearls, or costly array; But (which becometh women professing godliness) with good works.”
The Eighteenth Amendment banned the making, sale and transport of intoxicating liquors in the United States. It was ratified in January 1919 and came into force in January 1920. The Twenty-first Amendment repealed it in 1933.
A fixed standard, not a fashion
So the question really asks why Muslims do not move when the West moves. The answer is that Muslims were given a standard from God (﷾), and it is not put to a vote. The Qur'an says that no one can change God's (﷾) words. A rule that changes every thirty years is closer to a fashion than a law. A man is not disloyal to his country because he keeps his morals when his country changes its own.
“The word of thy Lord doth find its fulfilment in truth and in justice: None can change His words: for He is the one who heareth and knoweth all.”
Perspectives
The Islamic perspective
Muslims keep the values the West calls its own, from honesty to good neighbourliness. Their religion binds them to keep the law of the land, as the Prophet (ﷺ) taught. They differ on a short list of moral questions where the West has changed and Islam has not.
The Qur'an commands charity, care for parents, kindness to neighbours and the keeping of contracts.
The Prophet (ﷺ) said Gabriel urged kindness to neighbours so often that he thought neighbours would be made heirs.
The Qur'an binds Muslims to their agreements. The Prophet (ﷺ) told them to obey authority, except in a command to sin.
The Qur'an forbids intoxicants, gambling, sex outside marriage and interest, and commands modesty of both men and women.
The Qur'an says there is no compulsion in religion. It allows Muslims to deal kindly and justly with those of other faiths who do not fight them.
The medieval Church condemned usury as a sin, to the point of treating its denial as heresy.
The United States banned the making and sale of alcohol by constitutional amendment from 1920 to 1933.
The New Testament forbids fornication and asks women to dress modestly, as Islam does.
A moral standard given by God (﷾) does not change with each generation. So keeping it is not disloyalty to any country.