Salamun Alaikum.
Celebrating birthdays is not a religious matter, unless it is being performed in the name of religion or is clearly contravening religious edicts stipulated by the Quran.
It is up to the individual to make a decision based on the nature of the celebration, whether it will lead to undue societal pressure, the nature of the gathering, personal circumstances, what kind of social interaction this will entail and whether such a participation can be accomplished without compromising any other requirements of 'deen' mentioned in the Quran.
Certainly wishing someone well on their birthday and thanking God for the year of life He has granted them with His blessings is not going to contravene any religious decree to my knowledge.
A lot of this is judgment and intention based.
I hope this helps, God willing.
Joseph.