I am part of two institutions: Free Masonry and the Red Cross Order. I have no intention of abandoning them, given that they are philosophical- Freemasonry being a great school of learning that helps our fellow man. What to do? Can I reconcile these studies with the practice of Krishna Consciousness?

I do not see a serious problem in your affiliations. Lord Chaitanya, who brought the Hare Krishna Movement to the world, is Krishna Himself. So His authority is supreme. At the same time, other sources of knowledge can compliment our Krishna consciousness. The important thing would be to keep the teachings of Lord Caitanya and Srila Prabhupada as the primary point of reference, and keep as a core practice, bhakti-yoga, as they taught us. By doing this, you are free to improve and share their knowledge through your association with the groups you mention.