I flew BA SFO-LHR last week. My CX status and number was on the BP. In addition, the check-in agent also saw my MPC card. However, when I got to the lounge, I was still asked for my MPC card. The lounge agent volunteered the reason - the MPC status on the BP does not necessarily reflect my status on the day of travel. Afterwards, I have been to three BA lounges - two in LHR, one in EDI . They have not asked for my card anymore.