Ahh yes the Elders of FT have decided birthday greetings are not important to them and so therefore in an appreciation of diversity of opinion the loud voice of a few have determined therefore that birthday greetings should not be important to anyone.

The lack of birthday greeting is the challenge with BA in F. Unlike other airlines including BA, UA, QF, SQ they are unwilling or unable to tailor their service to individuals. While you can in some way understand that in Y, W or J you would hope in F that it would be part of the service experience and shows from a customer service excellence perspective the many challenges being experienced by BA and how a service centric culture is not at their core.

If you are not getting that personalised service at BA and you do get it from other carriers then I think it is reasonable to express a desire not to fly them and to seek alternatives. Just because personalised service is not important to you personally in F should not automatically invalidate this requirement for others.