Apparently the Swiss flag derives from a Roman banner granted to a sovereign city-state upon independence. The cross apparently does (tenuously) symbolize the Emperor as defender of Christianity (how ironic). Thus the Red Cross is twice removed from any religious affiliation.
[link|http://switzerland.isyours.com/e/guide/general/swiss.flag.history.html|http://switzerland.i...flag.history.html]
The St. George's Cross (red cross on white) is the "original" flag of England - combined with the Scottish St. Andrew's Cross (diagonal white on blue) we get the familiar Union Jack. Again there is a connection with Christianity but only indirectly - supposedly the resurrected Christ held a cloth so marked.
[link|http://www.baronage.co.uk/2002c/stgeorge.html|http://www.baronage....02c/stgeorge.html]