I am a fallen-away Catholic. I fell away before all the nonsense began, with the guitar mass and the hand shaking. As a southern woman, I will tell you, that I shake hands with no one, as I was never instructed that it was mannerly to do so, as a lady. I nod and say the appropiate words when introduced or greeted. Nothing annoys me more than to have a perfect stranger hold out his/her hand to me, as if I were a man. And it would be also true if I attended mass, still.
But I do remember my devout Catholic mother saying that she was annoyed by the hugging and hand shaking during mass in her later years, as she was in frail health, and did not want to be exposed to any more germs than was generated by the hacking and coughing of the congregation.
Besides, I think it is a silly gesture.