And lastly, if celebrating it is regarded as an innovation by you, Anybody that celebrates it in accordance to the doctrine of Islam: reciting the glorious Quran, the burdah, tasbih, lectures about his sayings and teachings, provision of foods and drinks, giving of alms, Then you don't need to Descriminate them, Afterall you are not Allah that will reward them nor the prophet that wil reject them.
Salam alaykum.

Salam Alaykum.
Celebrating the birth of the holy prophet Muhammad (pbuh) isnt an innovation, because even the prophet himself was asked by one of his companion why he fasts on Monday, and he said: I fast on Mondays, because it is on that day That I was born, its therefore meant to commemorate my birthday". Moreover there is no other better way of celebrating rather than remembering Allah, and giving back the glory to him. However following the sayings, teachings and actions of the prophet is compulsory on all Moslems as commanded by Allah in the glorious Quran ;

قُلْ إِن كُنتُمْ تُحِبُّونَ اللَّهَ فَاتَّبِعُونِي يُحْبِبْكُمُ اللَّهُ وَيَغْفِرْ لَكُمْ ذُنُوبَكُمْ وَاللَّهُ غَفُورٌ رَّحِيمٌ

Say: If you love Allah, then follow me, Allah will love you and forgive you your faults, and Allah is Forgiving, Merciful....Surah Aal-e-Imran, Verse 31.

So therefore, celebrating the mawlid Nabiy isn't an innovation, only if its celebrated in the wrong way which contradicts the doctrines of Islam. Reciting the holy Quran, the history of the prophet, the Burdah, Lecture about the teachings of the prophet which we need to learn are expected to be the programme of the day, provision of foods and drinks, giving of alms to the needy are those things that can be best used to celebrate his birth. Solallahu Alayhi Wasallam.