Geneva Conventions and United Nations Personnel (Protocols) Bill [Lords]

I seek a little clarification on two points. First, my understanding is that the symbol used by the Red Cross was a reversal of the national flag of Switzerland, so I cannot see the religious connotation. Secondly, I thought that the whole point of the red cross and the red crescent was that they were not aligned with a religion or a faith but used as symbols of humanitarian aid and assistance. If I am right in those two suppositions, how are my hon. Friends right in theirs?