I have a simliar situation. I tried to invite one of my friends to church and to Mutual. His parents haven't been interested. After a few more tries, I've realized I need to respect their privacy. Pray to our Heavenly Father to help soften their hearts about the Church if it is His will. And if it is, then they may change their minds about letting your friend come to Church activities.
Audrie F., 14, Utah, USA