What is the ruling of Islamic law on the responsibility of a group owner who prohibits what is forbidden in a mixed-gender group, if an acquaintance or love develops between the members?

It is permissible for a woman to create a religious group on social media, provided that it is under supervision and forbidden things are prohibited within it. It is preferable to limit participation to men, in order to avoid fitnah (temptation) and forbidden private conversations. If something forbidden occurs without your causing it, there is no sin upon you.