There are two occasions that birthdays are mentioned in the bible where someone did not get their heads removed.
The first is at Job 1:4 & 5 - And his sons went and held a banquet at the house of each one on his own day; and they sent and invited their three sisters to eat and drink with them. 5 And it would occur that when the banquet had gone round the circuit, Job would send and sanctify them; and he got up early in the morning and offered up burnt sacrifices according to the number of all of them; for, said Job, "maybe my sons have sinned and have cursed God in their heart." That is the way Job would do always.
In verse 1:1 of Job it call Job blameless and upright, and fearing God and turning aside from bad.
In some transalations the term "his own day" is translated birthday. Job and his children made a habit of recognizing and celebrating "his own day" or birthday.
The second occasion is at Luke 2:8-14 - There were also in that same country shepherds living out of doors and keeping watches in the night over their flocks. 9 And suddenly Jehovah's angel stood by them, and Jehovah's glory gleamed around them, and they became very fearful. 10 Buth the angel said to them: "Have no fear, for, look! I am declaring to you good news of a great joy that all the people will have, 11 because there was born to you today a Savior, who is Christ [the] Lord, in David's city. 12 And this is a sign for you: you will find an infant bound in cloth bands and lying in a manger." 13 And suddenly there came to be with the angel a multitude of the heavenly army, praising God and saying: 14 "Glory in the heights above to God, and upon earth peace among men of goodwill."
There was singing and praises sung on the day of Jesus' birth.
Also, in Matthew 2:2 - saying: "Where is the one born king of the Jews? For we saw his star [when we were] in the east, and we have come to do him obeisance." Matthew 2:10-12 - On seeing the star they rejoiced very much indeed. 11 And when they went into the house they saw the young child with Mary its mother, and, falling down, they did obeisance to it. They also opened their treasures and presented it with gifts, gold and frankincense and myrrh. 12 However, because they were given divine warning in a dream not to return to Herod, they withdrew to their country by another way.
Jehovah allowed people to bring gifts to the baby/child because he was born.
So, there are two occasions that birthdays were celebrated by servants of Jehovah.
I can't see why, when a person has lived 100 years that priviledge should be taken away.
Anyway, the WTBTS was found to be in an approved state in 1919 by Jesus and at that time they were still celebrating birthdays among various other celebrations.