It is well known that human relationships are very essential for healthy human and social life. We have non-Muslim colleagues, neighbors, partners, wives, in-laws, students and teachers, and many others who have many social and human roles in our life. We all share the same world.
First: It is relevant to state that there is no legal evidence in the Quran and Sunnah that forbids congratulating non-Muslims on their festivals.
Second: The act of congratulation has nothing to do with religious doctrines and one's cordial faith. In other words, when we congratulate people, it is not necessary that we approve of their achievements in life or their religious beliefs in religion. It is a pure way of compliment and amicability.
Third: Congratulation is a sign of noble morals and kindness and the Muslim is worthy of each aspect of nobility and high morals. As such, congratulating non-Muslims on their festivals, be they national, religious, or social is originally permissible, especially when we have a relationship i.e. marriage, neighborhood, colleagueship, fellowship, partnership, or other social relations, which require good communication.
Fourth: Each local religious or ethnic community has the right to celebrations and happiness so long as they do not harm others. Here, Islam does not forbid us from showing kindness to others, and congratulating non-Muslim citizens and neighbors is a form of religiously recommended kindness.
Fifth: Human kindness, friendship, and good treatment are Quranic recommendations, Allah says, “As for [the unbelievers who] do not fight against you on account of [your] faith, and neither drive you forth from your homelands, Allah does not forbid you to show them kindness and to behave towards them with full equity. Verily, Allah loves those who act equitably. Allah only forbids you to turn in friendship towards such as fight against you because of [your] faith, and drive you forth from your homelands, or aid [others] in driving you forth: and as for those [from among you] who turn towards them in friendship; it is they, they who are truly wrongdoers!” (the Quran, 60: 8-9).
Sixth: It is also clear that the Quran permits eating the food of the Christians and the Jews and the meat of their slaughtered animals, as well as marrying their females (the Quran, 5: 5). Now, how could you eat their food, be in their houses, marry their women, and have in-laws from them without maintaining good relations and exchanging greetings and congratulations? It is almost unreasonable and goes against the logic of things. Simply it is normal and religiously acceptable to maintain good relations and exchange greetings and congratulations with them without saying any forbidden statements or doing any unlawful acts.
Seventh: Marriage implies love, affection and mutual help and happiness between spouses; Allah says, “It is from His signs is that He created for you mates from yourselves that you may reside with them, and He placed between you affection and mercy” (the Quran, 30: 22). A Muslim man shall gently treat his non-Muslim wife and life partner, who is the mother of his children. The same goes true for her non-Muslim family. The simplest he shall do is the sweet expressions of congratulations and kindness, especially when they congratulate the Muslims on Islamic holidays. We shall say good words to all people (the Quran, 2: 83) and respond in more kind manners to their good things (the Quran, 4: 86).
In conclusion, Muslim individuals or organizations may congratulate non-Muslims on their occasions, national, ethnic, or religious, on condition that they do not say anything that violates the Islamic creeds or laws. They may say, “Happy new year” or “Have a nice feast” and the like. Likewise, they can exchange gifts, because Prophet Muhammad (Allah's peace and blessings be upon him) accepted the gifts of Non-Muslims, such as the Muqawqis, the great Copt in Egypt and others, provided that these gifts are not forbidden to the Muslim, such as wine and pork. Finally, accepting their gifs and eating their food have greater positive effects than congratulation itself, so it is logical that congratulation is absolutely permissible.