Yes, I believe that a person's religious faith is solely their responsibility. Faith is not something that should be influenced by anybody but yourself. Not only is it an individual's responsibility, it would be unconstitutional to say otherwise. Everybody should have the freedom to make their own decisions when it comes to matters of religion and faith.
While having a religious faith is important in many lives, having faith is a personal decision. Outside influences do play a part in the development of faith but it is up to the individual to accept or reject the premises that are presented. The development of faith or lack of faith begins in childhood and continues throughout ones lifetime. There are periods where they may be no faith and periods of extreme faith. However, for most a moderate faith seems to be adequate.
One's spirituality and faith are matters of personal experience and personal relationships with whatever God a person believes in. A religious faith is the responsibility of that person simply because spirituality or faith cannot be manufactured from human sources outside of one's own mind. There are 7 billion people on Earth and 7 billion different kinds of spiritual faith.
I believe one's religious faith is-- and should be-- solely a personal matter. While parents may attempt to instill a certain religious faith in their children, once the child is an adult, he or she should then make their own choice. Of course, any attempt by the government or other institutions to impose religion on people is improper as well, for something so personal.
In today's society we have what's called freedom, freedom to choose what we believe and how to treat others. I believe long ago that was not the case and many times religion was chosen for people. That still may apply today for some, but as an adult it is up to you and your responsibility to choose your faith and what you believe is right.