Same issue for me.
I am in household account with 7 people. I cannot select myself. My dad (head of household) is automatically selected and cannot be deselected.
I originally so the issue several weeks ago on my iPad but thought nothing of it as iPad has issues with several websites but the other day, it was also screwed up on my laptop and I called BA, they could not figure it out and sent t onwards to the IT department. I was told to make bookings over the phone and the delicate question of offline fees was answered by the agent stating that fees would not be charged and that the person making the booking can see my profile and the fact I cannot select myself.
This is only the issue when I select the Amex 241 voucher.