Treating "morality", "law" and "religion" as separate parts of human existence is a "modern western" phenomenon. There is no such separation either in the Bible, or the Qur'an.
There is "deen", which is often translated into European languages as "religion", but its meaning is different from what most modern Europeans1 understand by that word.
The root meaning of the word "deen" is that of "law", which has a broader meaning than the modern European understanding of the word "law", and includes not only criminal and civil laws enforced by a legal system, but also norms of approved and disapproved behaviour both towards other people and towards oneself, such as eating habits, personal hygene, ways of dressing - in fact, every aspect of human behaviour. So, some parts of that "deen" would be translated into European languages as "law", some as "morality", some as "religion", some as "personal hygiene", and some as "advice on healthy and successful living" - but even then the meanings of "law", "morality" and "religion" are not the same as understood by the Europeans.
While in a modern political state human actions are either legal (allowed) or illegal (punished by law), the Islamic (Shari'a) Law classifies human actions as (1) obligatory, (2) recommended, (3) allowed, (4) disapproved, and (5) forbidden.
The modern European understanding of the word "law" is anything that the government of a country wishes it to be. The government passes whatever laws are convenient to them, as long as the reaction of the people to these laws does not cause to the government more inconvenience than whatever advantage the politicians composing the government had hoped to achieve for themselves by passing these laws. This way of government has come to be known as "political convenience and social acceptability".
Examples of such politically motivated laws are taxation at the rate of 92%, which was introduced in the 1970's by the then Labour government in Britain, and the recently introduced law legalizing "homosexual marriages". The first one was justified on the grounds that the government wanted to "make the pips of the rich squeak", the second one to allow "homosexual couples to adopt children". The first one was motivated by hopes to achieve popularity by pandering to envy, the second to attract "the gay vote" of the homosexual "constituency".
By contrast, the laws of the Prophets of the Bible and the Qur'an are based not on whims and fancies of politicians, or even of "the majority", but on objective and impartial understanding of the universal human needs and the realities of the human nature.
Thus there are laws to prevent unjustified violence, to protect private property, to resolve disputes between people, to establish and protect the family unit, etc. Such laws are not for the benefit of some groups (or "constituencies") at the expense of others, they are applicable to all people in equal measure and are for the benefit of all.
The modern understanding of the word "morality" is what politicians and journalists choose it to be. Usually it is what is "politically correct". Whatever is really correct does not require qualification. So, "politically correct" is something the correctness of which cannot be asserted on its own merits. On its own merits it is not correct. But "politically" it is "correct", because it fits in with the political objectives of the politicians in power.
Thus the politically correct term for "sodomy" is "alternative life style". Such change of terminology makes sexual perversions "socially acceptable". One reason politicians want to make sodomy socially acceptable is because they want to attract the votes of the homosexuals - "the gay vote". And the other reason why some politicians promote "alternative life styles" is because they practice such "life styles" themselves. In the past they had to keep their depravity secret, now they can "flaunt" their perversions, giving them as reason for being elected to government offices.
By contrast morality of the Bible and the Qur'an teaches people to behave in ways which will be in harmony with Nature. Thus, people should use the various parts of their bodies for the purpose intended for them by the Creator. They should behave in such ways as to ensure health and wellbeing for themselves and for the Human Race as a whole. Thus, all the Prophets had condemned all forms of sexual activity outside of the normal (heterosexual) marriage. In the same way alcohol abuse and even gluttony (over-eating) are condemned by the Prophets, because they are harmful for people.
While in the modern political state the Human Reproductive Process ("sex") is used by political and commercial interests to take advantage of the people, the Qur'an provides practical ways of preventing abuses of the Human Reproductive Process.
The understanding of the word "religion" and of the elements of the Prophetic "deen" relating to worship and rituals is also different.
The modern European understanding of the word "religion", based on the post-Jesus Christianity, is that of a worship of a human-shaped deity, and a set of mystical rituals and encantations. Such activities were condemned by the Prophets as "idolatry". The Qur'an sees prophets, not as gods, or God's relatives, but as ordinary people with the rare gift of being able to distinguish the right from the wrong. Such people had a mission to guide the people of their time onto the Straight Path from the Path of Crookedness which people tend to follow in pursuit of their vain desires, urges and impulses. They never called on people to worship or deify their own personalities. Only God alone is worthy of worship. But this worship does not consist of rituals performed for their own sake.
The purpose of regular religious activities, like daily payers, as practiced or enjoined by the Prophets was educational. Thus, Muslim prayers include recitations of extracts from the Qur'an, while the Friday prayer includes a sermon (an educational lecture). By regularly reciting passages from the Qur'an and remembering that one is a part of God's creation one learns to live in accordance with the intentions of the Creator.
The Qur'an does not recognise any "mysticism", "magic" or "supernatural", but God's power is not limited by Man's imagination. So, what people might think of as magic or supernatural is either a deception or is perfectly natural, although contrary to their preconceived ideas of what is possible and what is not.
The principles of Islam, unlike the "dogmata" of Christianity and of other "mystical" religions, can be understood and explained logically and proved to be correct, but as understanding depends on the abilities, knowledge and experience of each person, and such abilities are always limited, people can benefit by following the principles of Islam even if they do not have complete understanding of these principles - just as children benefit from washing their hands, without understanding why it is necessary.
Thus, it is a mistake to see Islam as a "religion", as this word is understood in modern European languages. Islam is an applied science of Human Government consisting of Morality, Law and Social and Personal Philosophy of Life.
1) By "modern Europeans" we mean people whose view of life is the result of the "modern western culture", which has developed out of European Christianity to modern atheism or agnosticism and loose personal morality. This includes most Europeans, Americans, Australians, and "westernised" Africans and Asians.
For Morality: from its Origin to the Present Day see:
Morality: Past & Present