Some children can be by their temperament more timid than others. When in different situations it helps to assist them in negotiating it and stretching their comfort zone. Two stories come to mind. First is a little girl who every time a new person would come near, she would hide behind her mom's legs. The mom was embarrassed and said, "This is Becky and she is shy." This label gives a child justification for the difficult feelings they are having and it validates them if their is a word for it. What would be a good way to handle it is to say,"This is Beck my daughter. Becky, this is Mrs. Hanson who is a good friend of mine." Don't pick up the child but do squat down to be on the child's level. Make the contact short and positive. If possible you can even follow that up with having the child hand something to the person or walk with you both as you go somewhere or look at something. The idea is to demonstrate, a. this is an ok person. b. it is fine to be hesitant with people you don't know but that you can warm up more quickly with someone who is the parent's friend.
Another story is James. He was four years old and came to preschool with his father and cried every day for a week. He attached to me after I finally got his dad to leave but all he wanted to do was to sit and cry. No tears, but a heck of a racket. He held on to me tightly. After seeing for two days that my presence was reassuring but also a limiting factor in his ability to get engaged I started spending the first 3 minutes with him and then let him know that he had a choice. He coulds sit and cry or he could come with me as I went to play with children in other areas. He seemed stunned that I would leave him, but it only took about 2 minutes for him to come where I was. He then wanted to cling and cry where I was and I told him that if he wanted to cry he would need top go back where he was because there was no crying by the toys. Another thing I know is that children play and engage the world at a higher developmental level when they are taking on a role. This can be pretending to be a mom or dad of in some chases, Batman or Bob the Builder. That was just enough for him to go into any new situation and he could interact freely. The same child that could not walk up to someone as James would walk into situations and announce he was batman or Bob the Builder and have conversations with other children.
The main thing is to keep in mind that children are learning to trust themselves, others, environments, etc. and that usually it is a constant progression.
Is children's "shyness" a result of parents being overprotective? Yes and no. It can be heightened. Children take their cues from parents on how to act. If the child falls down and skins his knee does the parent rush to his side and try to sooth the hurt and calm the child? or the does the parent look at the knee, say, "ouch, I bet that hurts, lets go get it cleaned up." and calmly clean it up? One will heighten the child's dependence on the parent to take care of things and the other is reassuring while letting the child manage himself.