In Islamic history there are several auspicious nights and days, for example Allah-azwj Says:
إِنَّا أَنْزَلْنَاهُ فِي لَيْلَةٍ مُبَارَكَةٍ ۚ إِنَّا كُنَّا مُنْذِرِينَ [44:3]
Indeed, We, sent it down (Holy Quran) during a blessed night. Surely, We are ever Warning [44:3]
Similarly, Allah-azwj Says:
[21:107] وَمَا أَرْسَلْنَاكَ إِلَّا رَحْمَةً لِلْعَالَمِينَ
And We did not Send you except as a mercy to the worlds [21:107]
So, thanking Allah-azwj and gratefully acknowledging the ‘Mercy’ He-azwj has Bestowed upon us is Ibadah as we regularly thank Him for numerous bounties, we enjoy day and night – mentioning it more so on ‘Milad e Nabi’ which becomes on an auspicious day. Why do we say that? Allah-azwj Sends Peace on day when His-azwj Prophet-as was Sent Down, Recalled and will be resurrected.
[19:15] وَسَلَامٌ عَلَيْهِ يَوْمَ وُلِدَ وَيَوْمَ يَمُوتُ وَيَوْمَ يُبْعَثُ حَيًّا
And peace be on him on the day he was born, and on the day he was recalled, and on the day he would be Resurrected alive [19:15]
Also Allah-azwj Says:
[10:58]قُلْ بِفَضْلِ اللَّهِ وَبِرَحْمَتِهِ فَبِذَٰلِكَ فَلْيَفْرَحُوا هُوَ خَيْرٌ مِمَّا يَجْمَعُونَ
Say: ‘(All of these) is due to the Grace of Allah and by His Mercy – so it is by that, let them be rejoicing. It is better than what they are amassing [10:58]
In Ahadith ‘بِفَضْلِ اللَّهِ’ refers to bounties of Allah-azwj – i.e., the Holy Quran which was Revealed onto Rasool-Allah-saww – so بِفَضْلِ اللَّهِ’ is given to Muslims through the appointment of last Prophet‑saww (Mohammed Ibn Abd Allah) for that they should be rejoicing which is better than what they are hoarding.
Nonetheless, our way of rejoicing is to get engaged in the ‘Zikr, Hamd and Tahleel’ of Allah-azwj (Remembrance, Thanking and Praising) on more so on blessed days in order to refresh our memories of the special bounties of those days and nights, which are other than the ordinary days and nights in which we live in, i.e., Laila tul Qadr (The Night of Power) is better than a thousand months (97:3).
Zikr (remembrance) within the Islamic limits can be done in any day or night but if one specifically coincides it with a blessed ones of the Islamic year that cannot be called as a Bidah (heresy). One may or may not participate in such practices, as is the example of Tarawih[1], a practice which Muslims embraced during the time of second Muslim Caliph after the demise of Holy Prophet-saww. The same holds for adding ‘Assalatu Khairum Minan Naum[2]’ in the call for prayers in the morning Azan, among others.
So, lets respect the intentions of fellow Muslims without being critical of their way of offering their thanks and gratitude to Allah-azwj. In any case the outcome of Milad ul Nabi is positive, Allah-azwj is mentioned, love and treats of Holy Prophet-saww are highlighted, children learn Islamic history and get involved in the thanking and praising Allah-azwj – who Saved us from Hell Fire Through Sending to us His Beloved Prophet-saww who went through many hardships in the process of conveying the Divine Message and left behind the Holy Quran which is full of wisdom along with his-saww exemplary practices.
[1] Salat offered during the month of Ramazan, during which whole of the Qur’an is recited in many rakahs (cycles).
[2] Salat is better than sleeping