Is it permissible to continue communicating online with a young American Muslim man, hoping for marriage, after the parents refused due to cultural differences, despite feeling guilty and fearing religious transgression?

Praise be to Allah for your steadfastness and commitment to the hijab. We ask Allah to keep us and you firm upon the truth. Marriage to one who possesses religious commitment and good character is acceptable, for the Prophet, peace and blessings be upon him, said: "If there comes to you one whose religious commitment and character you approve, then marry him." However, conversations between young men and women via the internet are not permissible, as a preventive measure against evil. Your discomfort with them is a sign of your faith, so hasten to cut off this relationship, seeking Allah's pleasure.