Celebrating the Mawlid is a legitimate act of worship according to those who regard it as mustahabb
Question

I know that bid‘ah (innovation) refers to anything that has been introduced to Islam by way of worship. As that is the case, why do we describe the Mawlid as bid‘ah when it is merely a simple celebration that has nothing to do with worship? Of course some people quote as evidence the fact that the Prophet (blessings and peace of Allah be upon him) prescribed for us only two Eids, and no celebration on any days other than these two. Here I want to repeat myself and explain that celebrating the Mawlid is only an ordinary celebration that is free of any rituals of worship, and in that regard it is just like celebrating any other birthday.
Praise be to Allah.Celebrating the Mawlid (Prophet’s Birthday) is not only an ordinary celebration that has nothing to do with worship; rather for those who observe this custom it is a religious festival that is done as a means of drawing closer to Allah. 
This may be explained by noting the following points: 
Firstly: 
Those who celebrate this occasion and participate in it do that out of love for the Prophet (blessings and peace of Allah be upon him), and loving Allah and His Messenger are among the greatest acts of worship and signs of faith. So whatever is done for that purpose is undoubtedly done by way of worship and seeking to draw closer to Allah. 
Based on that, we may note that the Companions of the Prophet (blessings and peace of Allah be upon him) had a greater love and respect for him, and were more aware of his rights, than those who came after them, so whatever did not constitute part of the religion for them does not constitute part of the religion for those who come after them. 
It was this principle that ‘Abdullah ibn Mas‘ood (may Allah be pleased with him) quoted to the people of the halaqah who had gathered to remember Allah in the mosque, and were all counting their dhikr with pebbles. He said to them: By the one in Whose hand is my soul, you are either following a path that is more guided than the path of Muhammad (blessings and peace of Allah be upon him) or you have opened the door to misguidance! 
They said: By Allah, O Abu ‘Abd ar-Rahmaan, our intention was nothing but good. 
He said: And how many people who aimed for good never attained it! 
Narrated by ad-Daarimi in his Sunan (210). 
Secondly: 
If a celebration is held every year, that makes it an eid or festival, and festivals are religious symbols. Hence you find the People of the Book regarding their festivals as holy and celebrating them. 
Shaykh Naasir al-‘Aql (may Allah preserve him) said: 
Festivals come under the heading of religious symbols and rituals, like facing towards a particular direction in worship, prayer and fasting; they are not mere customs. This is why the issue of resembling and imitating the disbelievers in them is so serious. Similarly, introducing festivals that were not prescribed by Allah is tantamount to ruling by something other than that which Allah has revealed, speaking of Allah without knowledge, fabricating lies against Him and introducing innovations into His religion. 
End quote from Muqaddimat Iqtida’ as-Siraat al-Mustaqeem (p. 58) 
Thirdly: 
Abu Dawood (1134) narrated that Anas (may Allah be pleased with him) said: When the Messenger of Allah (blessings and peace of Allah be upon him) came to Madinah, they had two days on which they would play. He said: “What are these two days?” They said: We used to play on these days during the Jaahiliyyah. The Messenger of Allah (blessings and peace of Allah be upon him) said: “Verily Allah has replaced them for you with something better than them: the day of (Eid) al-Adha and the day of (Eid) al-Fitr.” Classed as saheeh by al-Albaani in Saheeh Sunan Abi Dawood. 
If merely celebrating a festival was a matter of custom, and had nothing to do with worship or imitating the disbelievers, then the Prophet (blessings and peace of Allah be upon him) would have left them to their play and entertainment, because there is nothing wrong with playing, or permissible entertainment and fun. 
But as the Prophet (blessings and peace of Allah be upon him) told them not to celebrate the occasion of a festival by way of playing, although it does not seem that it was singled out for any act intended to draw closer to Allah or any act of worship, then how about those who do that by way of seeking to draw closer to Allah or by way of worship? The Messenger of Allah (blessings and peace of Allah be upon him) said: “Whoever introduces into this matter of ours something that is not part of it, it will be rejected.” Narrated by al-Bukhaari (2697) and Muslim (1718). 
For more information, please see the answers to questions no. 10843 and 128530.
And Allah knows best.