Parents who "demanded" access to the treatment room during a procedure were in effect saying that they did not trust the doctor to render proper treatment. Such attitudes are easily transmitted to a child, and for a dentist, they usually spell trouble for all concerned. My husband learned that trying to deal with a tense, distrustful parent usually wasn't worth the effort, and he referred those cases out to a pediatric specialist.
Exceptions to the "no parents" rule did exist. Generally, these were parents who were patients themselves and who were comfortable with the doctor. A parent who casually observed and chatted during a procedure presented no problems, as he/she transmitted an attitude of relaxation and trust to the child.
Oh.....and learning that a child was home schooled never raised any "red flags" for my husband. In fact, he found most of his home schooled patients to be quite exceptional and delightful. As long as a child is happy, well adjusted and well cared for, there are no "red flags" to be raised.