This is a complex question because here the term of risk might be understood in 2 ways. You are asking the risk associated to the action of "communicating one's birth date to a company".
Are you talking of the overall risk associated to the final result of this
operation or are you talking of the added risk associated to this sole action.
From the details of your question, you are asking an evaluation of the risk just added by this operation.
Since a birth date is a public information, neither secret nor revocable,
you can't change in any way the overall risk associated to this information.
The risk associated with this operation is then: 0.
This look chocking, but this is due to the fact that "communicating one's birth date to a company" is a risk before the action of one communicating his birth date.
The overall risk associated to communication of birth date might be seen as
a simplified formula:
false secret + bad security + crosscheck hunt + personnal communication
and my estimate of these in terms of added probabilities of bad results occuring is:
false secret: x
+ bad security: y
(this y isn't independant x)
+ crosscheck hunt: z
risk added by hunter of different public
information to build a correct identity to attack
companies promoting false secrets
+ personnal communication: t
Total probability of bad: p = 1 - (1-x)(1-y)(1-z)(1-t)
(My personnal raw estimate is that x ≃ 0,1, y ≃ 0,4, z ≃ 0,2, t ≃ 0
which leads to a p ≃ 0,6)
For the same reason, from my personnal point of view,
the overall risk associated with the idea that a
birth date is a secret and could be used as an authentication is of: 1 (= probability of bad event = 1 x perimeter of impact = max).
My bank is using my birth date as an identification mechanism.
I explained them why I trust them less than others because of this false secret they are selling to naive customers and the risk they are creating.
They didn't change. They registered the information very politely.
The risk that I switch bank is increasing every day.
The risk that this poor practice become public increase every day.