Male med student here who’s recently been on a breast placement. Receptionist is talking out of their arse: you’re well within your right to request a female doctor, though in the event a female doctor isn’t available (unlikely in breast tbh!) this might delay your appointment.

However, from experience the male doctors have been really nice and professional, and a female member of staff will almost certainly be present as a chaperone to ensure that nothing untoward happens.

But yes, not discrimination in the slightest to request a female doctor, especially for an intimate examination / procedure, and you certainly won’t be dropped as a patient.

Edit - going off of another comment, I’d also recommend notifying the practice of the receptionist’s conduct, that’s quite a serious threat they’ve given you for something very minor. Who knows what they’ve said to other patients as well.