Imam Muslim related, through the route of Jarir Ibn ^Abdullah, the Prophet said:
which means: <> There are two types of innovations mentioned in this hadith: the innovations of guidance and the innovations of misguidance.
t complies with the Qur’an, the Sunnah, the Ijma^ (scholarly consensus), and the sayings and practices of the Companions is an innovation of guidance, and what contradicts the Qur’an, the Sunnah, the Ijma^, and the sayings and actions of the Companions is an innovation of misguidance. This definition of the two types of innovations was given by many knowledgeable and trustworthy scholars of Islam; among them Imam ash-Shafi^iyy, Imam an-Nawawiyy, al-Bayhaqiyy, and the Hafidh, Ibn Hajar al-^Asqalaniyy.
It is apparent Muslims have not gone astray in celebrating the birth of the Prophet, or saying salat and salam after athan, based upon the aforementioned hadith, because the deeds practiced during this event are considered rewardable by the standards of the Religion, and in line with the definition of innovations of guidance.
Unfortunately, there are some people who misinterpret a sahih hadith related by Abu Dawud: which means: <> Those who are misguided interpret the word (kul) as `every’ and thus claim this hadith means: "Every innovation is an innovation of misguidance.
Their claim is unfounded for two reasons. Linguistically, this hadith is similar to the hadith related by al-Bayhaqiyy:
which clearly does not mean: “Every eye gazes the look of the adulterer;” rather, “Most people are guilty of the forbidden look.” The person blind since birth would surely not have the forbidden look, and it is known the Prophets would never commit such an abject sin. The word (kul) as used in both hadiths refers to `most,’ although it can mean “every” it does not mean this in all cases.
As a matter of fact, in the explanation of Sahih Muslim, an-Nawawiyy said: "The saying of the Prophet, sallallahu ^alayhi wa sallam, is among the terms which are (^am makhsus) i.e., a general statement giving a specific meaning; which is a known field in Islam, and the meaning of the hadith is “most innovations are innovations of misguidance.” This field is seen in the Qur’an in Ayah 3 of Surat al-Ahqaf:
which means the wind Allah sent as punishment to the people of ^Ad demolished most of the things.
To accept the meaning: “Every innovation is an innovation of misguidance,” as the meaning of the sahih hadith related by Abu Dawud would negate the sahih hadith related by Imam Muslim which specifies two types of innovations: the innovations of guidance and the innovations of misguidance. In the rules of the Religion it is not permissible to interpret two sahih hadiths in contradiction to one another, therefore we know the true meaning.
Although most innovations are innovations of misguidance, there are numerous examples of Religiously acceptable innovations. During the Caliphate of ^Umar Ibnul Khattab, ^Umar initiated the gathering of people in Ramadan to pray the Tarawih Prayer in congregation. When he saw the people performing this prayer in congregation he said:
which means: “What a good innovation that is!” The high status of ^Umar Ibnul Khattab is known, thus it is important to point out ^Umar used the explicit term “innovation” in his praise. If all innovations were misguided–as some claim–^Umar would not have innovated this practice, nor expressed this praise, yet both al-Bukhariyy and Muslim related this incident. During the era of the followers of the Companions of the Prophet, another praise-worthy innovation took place. Initially, letters like the ba, ta, tha, and ya, did not have dots above or below them. This practice of distinguishing between the letters by using this notation began after the time of the Prophet.
Since the time of the Prophet, many innovations have been adopted. Remembering the birth of the Prophet by doing rewardable deeds is a praise-worthy innovation. It is an honorable event and special to Muslims throughout the world. We rejoice in being members of the greatest nation of Islam–the nation of Muhammad–who was the best Prophet and the best creation of Allah. In Surat Al ^Imran, Ayah 110, Allah said:
which means: [You are the best of nations brought forth to the people; bidding the lawful (ma^ruf) forbidding the unlawful (munkar), and believing in Allah.] This verse means this nation is the best of nations by virtue of its Prophet," as explained by the scholars of Islam. Muslims are thankful to Allah for the blessings of Islam and for being among the followers of Muhammad. In Surat Al ^Imran, Ayah 31, Allah said:
which means: [If you love Allah, then follow the Prophet, and Allah will love you.]
I hope that helps.
Allah knows best.