Wa`alaykum As-Salamu wa Rahmatullahi wa Barakatuh.
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 a lot for your question, which reflects your care to have a clear view of the teachings of Islam. Allah commands Muslims to refer knowledgeable people to become well-acquainted with the teachings of Islam in all aspects of life.
We would like to stress that Islam teaches Muslims that they should never take non-Muslims as patrons against other Muslims. However, Muslims should have good relations with all people. At school, at work, in your neighborhood, etc., you should be kind and courteous to everyone. Muslims are allowed to have non-Muslims as friends as long as the Muslims keep their faith and commitment to Islam pure and strong, and as long as those non-Muslims do not fight Muslims.
In his response to your question, Sheikh Muhammad Al-Mukhtar Ash-Shinqiti, director of the Islamic Center of South Plains, Lubbock, Texas, states the following:
The problem does not lie in making alliances; the issue has to deal with taking allies against other Muslims.
The Prophet (peace and blessings be upon him) made peace treaties with some pagan tribes and others. He also did the same with the Jews of Madinah and the Christians of Najran. However, he did this for the sake of Islam and Muslims.
Therefore, befriending non-Muslims and building political alliances is not forbidden per se; they are based on the goal and the possible consequences.
The type of relationship forbidden by the Qur'an has to do with Muslims' building alliances with non-Muslims in order to harm other Muslims, for Muslims are brothers and sisters to one another and protecting one's brothers and sisters is obligatory in Islam.
That is why Allah says [Let not the Believers take Unbelievers as allies against (other) Believers] (Aal `Imran 3:28).
So "against (other) Believers" is the key to understanding the whole issue of walaa' (loyalty) and baraa' (dissociation) in the Qur'an.
I am aware of the sad reality you have touched upon in your question.