Is it safe to have a mammogram during pregnancy?

No. In general we try to avoid xrays if possible during pregnancy. If imaging of the breast is needed during pregnancy a breast ultrasound is a better choice. If you are referring to an annual screening mammogram it should be done before or after pregnancy.
Prefer not to. We prefer not to do mammograms during pregnancy due to radiation and because of changes seen in breasts. The increased lumpiness makes the mammogram more difficult to interpret. An ultrasound is safe.
Yes. From the American Association of Physicists in Medicine( "It is safe to have a mammogram while pregnant. The radiation dose received by the fetus is estimated to be extremely small - 60 times less than the dose received by the patient from one month of background radiation." .