Wa `alaykum as-salamu warahmatullahi wabarakatuh.
In the Name of Allah, Most Gracious, Most Merciful.
All praise and thanks are due to Allah, and peace and blessings be upon His Messenger.
Dear brother in Islam, thanks for your question. May Allah bless those who seek knowledge to clear misunderstanding.
It is true that customs and traditions differ from one society to another. However, Islam constitutes a bond that unites all Muslims. The spirit of brotherhood and collective submission to Allah and His injunctions, if truly practiced and faithfully observed, are sure enough to eradicate such differences. When a dispute erupts owing to the difference in customs and cultural backgrounds, it should be settled according to the rulings of the Shari`ah. Once the Shari`ah decides the matter, none should feel unease or claim arrogant superiority.
Answering this question, Zienab Mostafa, a prominent Muslim Scholar and Da`iyah, said:
Islam has put an end to racism and tribalism. It has united us all under one banner. In the Prophet's Last Sermon, it is stated that "there is no superiority for an Arab over an Arab, for a white person over a black one except in terms of piety (taqwa )". There is no text whatsoever stating that an Arab must not or should not marry a non-Arab. Therefore, we should fight racism and tribalism that have caused disunity among Muslims. We should better follow the Prophet's example in his relationship to Marriyah who she was not an Arab.
As for understanding each other better, it is the harmony between human values and personal traits that help marriage to be successful and not the culture. There are so many Arabs who got married but their marriage collapsed even though they were from the same culture.