As I've already written, I think it's important that women are given a definite choice. Personally, it doesn't bother me in the slightest. I've never found mammograms that uncomfortable and since I had breast cancer, I've become used to having my breast touched and manipulated by loads of different medics. I didn't keep a tally of the number of males, but I reckon it was about half. The doctor who did the initial biopsy after a suspicious area was spotted was male, as was the doctor who inserted wires so the lesions could be located easily. The surgeon and his assistant who performed my surgery were male, as were some of the radiographers who administered radiotherapy, which involves moving the breast to the optimal position. I then had my other breast reduced, so that it matched - both surgeons were male and I had to stand while they draw little marks with a Sharpie pen on my breast. It didn't occur to me once that these people were male - they were doctors as far as I was concerned.
I was far more embarrassed when I had a cyst removed from inside my vagina. I was in stirrups on an operating table and, looking down, all I could see was the male surgeons head between my legs.
Nevertheless, it is important that as many women as possible have mammograms and I think it should be made quite clear beforehand that there is an option to have a female mammographer.