These notes below are on the Manchester airport Web site. The dose you receive is minimal, much less than you will get from taking the flight itself. You can't choose to opt out.
Body-scanners & Pregnancy
Body-scanners are now being used at Manchester Airport to allow security checking of a person without the need for a physical ‘pat down’ by a security officer.
Many official, independent international bodies including the Health
Protection Agency (HPA) in the UK have assessed the risks from the scanners. They are approved for use for all passengers including expectant mothers.
The emissions received from the scanner are a very small fraction of that received every day from natural sources.
These emissions are enough to pass through clothing but not high enough to pass through the body and therefore pose no risk to the mother or baby. The reflected X-rays are then collected and transformed electronically into an image of the body shape.