Yes, mix apples and oranges here. If you search this forum, you will find many threads where brothers and sisters post amazing ideas of how muslims should behave in universities/schools. We might go where non muslims go for jobs/education etc but even there muslims are muslims, and do their best to remain muslims. A simple way to avoid greeting Happy Birthday is, I just tell my friends, May Allah bless you today and always. We are always encouraged to do duas for our brothers/sisters right?
It is believed that Kuffar celebrate and wish happy birthday hence it is the culture of a kuffar