Is it permissible for a Muslim woman to associate with non-Muslim women in forums and social networking sites?

The default rule regarding befriending a disbeliever is prohibition, unless the intention is to invite them to Islam. Friendship on forums does not necessitate real-life friendship. It is permissible to open an account and add those from whom one expects benefit or interest, even if they are deviants, provided that the account holder is a person of faith, righteousness, and uprightness, and knows that they will be influential and beneficial, while taking precautions and being wary of examining the doubts of disbelieving women.