I'm pretty flexible about parents sitting in on lessons. I do require a parent to sit in the first 2 or 3 weeks of any new student's lessons. I think it's good for the parent to see how I teach, to have me explain the home practice expectations, and to get a general understanding of what goes on during the lesson. After the first couple of lessons, they know they are welcome to come in any time, but it is no longer required. I don't think I've ever had a parent sit in after the required beginning lessons.
Some parents do wait in the adjacent room, rather than sit in their car, and that's fine with me too. They can hear but not be seen.
I require 4-5 year olds to have a parent attend every lesson, and the parent learns right along with the child. I love teaching that way.
Starting this fall, I'm considering having one lesson each semester that is "parent's day" on which the parents are specifically requested to sit in on lessons, just to increase their understanding of lessons, to see some of the creative things I do, and maybe do some student/teacher duets for the parent. I'd make it optional, but hopefully many would want to attend.