The Bible's stance against false prophets is quite clear:
Deut 18:22
But the prophet who presumes to speak a word in My name, which I have not commanded him to speak, or who speaks in the name of other gods, that prophet shall die.'But the prophet who presumes to speak a word in My name, which I have not commanded him to speak, or who speaks in the name of other gods, that prophet shall die.'
Eze 14:10
And they shall bear their iniquity; the punishment of the prophet shall be the same as the punishment of the one who inquired,
Rev 19: 20
And the beast was taken, and with him the false prophet that wrought miracles before him, with which he deceived them that had received the mark of the beast, and them that worshipped his image. These both were cast alive into a lake of fire burning with brimstone.
Birthdays:
There are no explicit sanctions against birthday celebrations in the Bible.
Christmas:
There are no explicit sanctions prohibiting the celebration of Christmas in the Bible. On the other hand, there is more than enough historical evidence to link ancient Christmas celebrations with the celebration of various winter festivals, most notably Dies Natalis Solis Invicti (Birthday of the Unconquered Sun - Roman), Saturnalia (Festival of Saturn - Roman), and Shabe-e Yalda (Longest Night of the Year Festival - Persian). However, for most people, the pagan symbolism that was once conflated with Christmas has long been forgotten.
What's worse, celebrating birthdays, Xmas, or following false prophets? Well, concerning birthdays and Christmas, it is up to the discretion of the individual Christian. Remember Paul's words in 1Cor 10:31:
Therefore, whether you eat or drink, or whatever you do, do all to the glory of God.
As for false prophets, the only road that lies before them is death.