Is it permissible to create an Islamic chat program that prohibits pornographic content and content insulting the Messenger (peace be upon him), knowing that there will be private rooms that cannot be monitored and public rooms that might be used for music?

There is no harm in establishing a da‘wah forum even if individual wrongdoings unknown to the administration exist. However, if the forum could only exist with these wrongdoings, yet it achieved great legitimate benefits, then there is no harm in establishing it. This is because when benefits and harms conflict, harms may be tolerated for the sake of achieving predominant benefits, provided that effort is exerted to prevent the forum's use for what is impermissible شرعاً and that regulations are put in place to prevent violations.