those who ask "Why do Muslims show great love for and interest in those people with whom they have only recently become acquainted?"

Love is not an emotion that one can attain by one's own willpower or something acquired by force; rather, Allah inspires it in one's heart. A believer does not need to possess sublime attributes or distinctive abilities to feel affection for someone else. A person of faith recognizes the beautiful things created by Allah, down to their most delicate features, and so can see a person's good and beautiful aspects, as well as his or her unrevealed features, more clearly and rapidly and therefore behaves accordingly.
Believers may show affection to someone who has not adopted the Islamic way of living, for some features that comply with the Qur'an's morality in that person (e.g., naturalness, sincerity, cleanliness, intelligence, beauty, intimacy, and sympathy) may arouse a natural affection in their hearts. That person may also have attributes of good character, although he or she is not fully aware of them. All of these characteristics are sufficient to develop a sincere affection for that person, for they are, in actuality, beauties created by Allah. For this reason, such affection is not directed toward that person; rather, it is directed toward Allah.
Allah inspires a profound love of beauty in all believers' hearts. While mentioning Prophet Yahya (John) (pbuh), Allah states: "We gave him [Yahya] ... tenderness [for all creatures] and purity from Us." (Surah Maryam, 13) All believers who follow in the footsteps of the Prophets feel this tenderness for all creatures. In fact, Allah states: "As for those who believe and do right actions, the All-Merciful will bestow His love upon them." (Surah Maryam, 96) As an expression of this love, believers always honor other people and avoid offending or dishonoring them in any way. In brief, believers do not behave in an insincere or artificial manner with others. Provided that a person is sincere, his or her pursuit of the right path and curiosity indicate consciousness, which is a positive attribute. Even a person's frank inquiry about Islam, one that is divorced from any prejudice or ill intentions, is sufficient to earn the believers' sympathy.
Meanwhile, believers do not pretend to love somebody if they really feel no love for that person in their hearts. They do not show love superficially and unwillingly to people who is not worthy of love. Under the guise of love,  some people who are ignorant of religion establish bonds with people based upon mutual interests that are not always of a material nature. Provided that the person in question somehow satisfies that person's ego, this bond may turn into a habitual relation. The complicated emotions arising from benefits, habits and egoistic dependence differ greatly from the mutual love and interest among believers. Such relations are based upon mundane interests and therefore are doomed to failure, as the verse below states:

And he [Ibrahim] said: "For you, you have taken (for worship) idols besides Allah, out of mutual love and regard between yourselves in this life. But on the Day of Judgment you shall disown each other and curse each other. Your abode will be the Fire, and you shall have none to help." (Surat al-'Ankabut, 25)

The major feelings that impede love are pride and jealousy. These feelings, which are prevalent among societies ignorant of religion, often hinder people from seeing the good attributes in others and from taking pleasure from them. But those who have faith, and thereby are free of jealousy and pride, find it easy to appreciate and praise people's good characteristics, all of which they attribute to Allah.
For this reason, those who have only recently become acquainted with believers will notice that they have entered an environment that is quite different from the one to which they are accustomed. While they were accustomed to mostly impolite, indecent, rude, insensitive, derisive, insincere, self-seeking, and hypocritical people, they now find themselves surrounded by people who notice their good characteristics, (of which even they might be unaware), and who judge them according to these favorable traits. However, they have to be aware of the importance of this blessing from Allah and have to thank Allah for granting them this true sincerity, friendship, love and trust which they cannot see in the societies ignorant of religion.