Leendert,
You shouldn't need to synchronize users when using JFBConnect, but it certainly shouldn't cause problems if you do. We've never heard of this problem and will have to look into it more. Just to make sure:
* You are importing the birthday from FB into a "date" field
* The date is correct before synchronizing
* The date changes afterwards
As for questions:
Is this for every user (if you've tested multiple)?
If you synchronize again, does it change again?
Finally, is there a reason your synchronizing in the first place? Generally, this shouldn't be necessary to do commonly in any CB configuration.
Thanks,
Alex