Girls/Women should also be asked to get tested, it's not offensive to look after your own health. In fact, any girl/woman should see that as a sign of someone being responsible. It does not mean someone is being accused of promiscuity, as STDs are not only passed on through intercourse.
A man asking this of a chaste woman from a practicing family will most likely get chased away. It is offensive because whether he intends it or not he is implying she may not be chaste. People will automatically link "STD" with zina/faahisha and not medical malpractice.