They were allowed to travel relatively freely. It is common knowledge that women were typically excluded from religious ceremonies during Biblical times. A woman sometimes dressed like a man in order to gain access to the worship service. This interpretation has particular appeal because the verse is first directed at women, and then at men. In most verses, the important point is first followed by less important points.
Most experts fail to even mention transvestites.
The other 29 verses of the chapter are largely ignored, yet two seem curiously related. You must sew tassels on the four corners of your cloaks. One might ask why there isn't a great disturbance about the blended fabrics commonly worn today by both men and women. Other matters that the world pays little attention to get far more emphasis in the Bible. Well, for anyone willing to take an unbiased view, there certainly isn't a Biblical case against cross-dressing.