One of the areas that I spend a lot of my time doing my "hard thinking" is in this subject.  MedicalMissions seeks to ensure that any team needing providers gets them and that any provider looking to volunteer finds a place to serve.  We don't exclude any participation nor do most of our senders.  Most sending organizations include foundational principles and policies but don't exclude anyone from participating as long as they are comfortable with the team environment.  

I see a definite trend regarding the opening of volunteer teams to peoples of all faiths, creeds, etc.  Again, the organization typically has their unique beliefs and ancillary efforts but as long as they are clearly articulated in advance, most end up with a wonderfully diverse team of people and talents.

I'd love to hear other folks thoughts and experiences and welcome any questions you might have for me.

Our organization, AidWEST, is deliberately inclusive; everyone has something positive to offer during a crisis, if they are directed well.  Also we were specifically interested in being inclusive in terms of faith/non-faith, and of course in gender, culture and ethnicity.

As a chaplain I got very used to working with people of all faiths. Some people may not be comfortable with an ordained woman, but most people don't care as long as we don't get paid. <grin>  I know some countries where people of faith have a very difficult time, but for important work, it mostly works out.