Everything certainly is a human construct. You use Law and morality as an example. Law is to keep those that will disrupt in line and give them consequences. Morals are a tool of judgment and are meaningless in my mind as a guideline for anything. They change from person to person and are even more in flux than laws.
Yes people are communal but was it the nature of language that eventually did divide? What caused humans to design nations and borders? What causes others to judge someone by the shade of skin, accent, or religion. How many gods do you think there might be? Each religion would have there own that agrees with them. So why is there this religious feeding frenzy. It is because humanity has chosen what and how they will believe. Religious action is a human construct as well.
Law fulfills many functions.
I am a bit taken aback by your wholesale rejection of morals. Moral guidelines like that you shouldn't steal, kill, rape, cheat, etc, seem to me to be a bit more stable and less meaningless than you suggest. Ultimately morals form the basis for law and society as a whole and - unline Margaret Thatcher whom I like on many other scores - I do believe there is such a thing as society.
I think it is meaningless to look for a "cause" why people divide along ethnic, cultural, linguistic, religious, political lines. It just happens and is perfectly natural.