You say that your daughter's generation falsely believes that your organization is feminist and that they state wrongly that feminism is a belief system in accordance with Christianity. You assert that your generation correctly believes that feminism is problematic, bashes men, and has fascist tendencies.
I am of your daughter's generation, I suppose, if we must sort people by age, and gender, and country, and all of these other artificial divisions, and in that artificial division you have created, it is not "us" who have feminism wrong. You have mischaracterized feminism and even implied that feminism is a profane word we should avoid using.
The following is a description of my logic for supporting Christian feminism. Those not adhering to Christianity have a completely different process for arriving at feminism. Because you identify as a follower of Christ, I hope that you will find it clarifying.
Given that all good things come from God
Given that humans are created in the image of God
then the Christian God must have all of the positive characteristics culturally attributed to both genders
and from that it follows that as we become more like Christ, we will attain more of the positive qualities ascribed to both genders
Given that God created humans in the image of God
Given that God sent Jesus to save all humankind
Given that God calls all humans into a relationship with the Trinity
Given that Christians are called to proclaim the Gospel and use the talents God has endowed them with to advance a world of peace, justice, and unconditional love
then it follows that Christians of every gender must advocate for humans of every gender to be treated as having inherent value and thus afforded all rights and opportunities associated with such value.
In truth, the Christian feminism your daughter's generation holds is the belief that many women may be called to more than cleaning house and being sexually available to a male partner - a belief I know that your nonprofit shares. It is the belief that current constructions of masculinity prize aggression, hypersexuality, and stoicism, and that hurts men and women both.
Christian feminism calls for vulnerability for all, protection (physically, emotionally, and spiritually) for all, and says that men too, are harmed by an artificial binary wherein men are strong and women are sensitive.
You know that many of your women are physically, mentally, emotionally, and spiritually very strong. You know that many men are compassionate, sensitive, nurturing.
I don't see how acknowledging the soft side of men or the strong side of women or the coexistence of both of this is twisting what humans - male and female - were created for, as you imply it does. We don't need a new word to use instead of this supposedly profane "f" word, though some have been using "equalism," if you are still in search (problems with framing the issue as equalism will be deferred to a later post). We don't need a new word. Those who have distorted and denigrated the concept of feminism need new insight. I hope that this message provides a little, as the word itself is viable and vibrant and not going away.
In fact, the feminist movement is the reason that my generation generally has been able to take for granted that we will attend university and get the training to pursue our callings. It is the reason we have a voice for the women you serve who have no voice. It is probably even the reason you are able to head an influential nonprofit. It is the reason we have female legislators to pass laws to protect women. It is the reason that you and your women in the United States can hold your own paychecks and bank accounts instead of giving their income to a father or husband. It is the reason that you and the women you protect who become US citizens can vote. In short, it is the reason that women in the United States are (mostly) no longer viewed as property, a belief your organization hopes to spread to the developing world.
This is why "my" generation says that your nonprofit is feminist. We value the dignity that your organization gives to all people. We see your team as helping all whom they help to move closer to God and closer to their God-given callings. I don't know what would be profane or fascist about that.
In short, you are a feminist, whether you believe it or not.