I humbly differ with the referred to opinion on the ground that the AHadith quoted to prove the notion do not lead to the conclusion. Let us consider the AHadith presented in favour of the opinion.
The words ‘into this matters of ours’ used in the first Hadith are worth pondering. These words clearly indicate that the Holy Prophet (sws) is talking about something specific. The same is the case with the second tradition. Here again you find the words ‘in accordance with our affairs’ which clearly indicate to it being specific. We will try to determine what that specific thing is.
We know that the only thing that the Holy Prophet (sws) brought is the religion of Islam. We also know that all religious matters should spring from the fountainhead of the Holy Qur’an and the Sunnah. He should not have forbidden us from other realms of affairs. If so the religion would be an impediment in progress. We would not even be able to use all are kitchen utensils we use today. Therefore, the Hadith should be interpreted in context of religious teachings and practices. The Holy Prophet (sws) only forbade innovation in religion not in all human activities and disciplines.
Now the question arises whether celebrating birthdays is an act religious in nature. The answer to the question lies with those who celebrate it. They simply express their joy or express their gratitude towards the Almighty. The act in its nature is not a religious act rather it is a social custom.
A legitimate objection would be that celebrating the birthday of the Holy Prophet (sws) very likely is an act that can be easily (not necessarily) be associated with religion. We regret to say that often it is deemed a religiously rewarding act. However, celebrating our own birthday could not and should not be given a religious tint. This is a social act not religious. Therefore, there may be other faults in the custom but it can no way be deemed an innovation in religion. Its prohibition must be mentioned explicitly in the Shari‘ah. We cannot hold something prohibited for ourselves. We cannot extend the effect of a ruling issued by the Qur’an or the Sunnah to what it has no relevance with.