When doing a pose like this, there are three main areas of potential groin discomfort for me.
- Discomfort from the upper pubic area pressing against the ground: This area typically has a layer of fat, covered by hair. Pressing of the flesh, and pulling of the hair, can be painful, something both men and women will potentially experience. My usual of dealing with this is avoiding underwear that is more likely to bind to the hair, and when I feel pressing discomfort, focusing more on lifting my torso rather than pushing my hips down.
- Compression of the penis against the floor: This doesn't happen to me very often, but if I'm more pulled to the front, this can be an issue, particularly if there's any blood engorgement involved. My usual solution is to either tuck (ensure that the penis is rotated more down and back) beforehand, or to do the movement in a rolling forward fashion that makes the friction of the floor move everything away. Also, I've found this is more prone to happen when wearing tighter "briefs" style underwear.
- Testicular compression: This is the one that I feel is most dangerous/painful. If you get your testicles trapped between you and the floor, or between your legs when they're squeezed together, it can be very painful, and it is possible to cause yourself permanent injury. First off, as with the prior point, tuck. Secondly, spread your legs a little to give yourself room to let your testicles move away from the floor, and disabuse yourself of the practice of squeezing your legs together to get a little bit more lift in the torso.
Hopefully,that helps you in your yoga practice. Personally, I've found that you get used to the movement pretty quickly, and protecting yourself from injury or discomfort becomes second nature.