While I can only speak for LXA and Masonic Scotish Rite, I think and feel whether a Greek Organization will have some relegious conotation is the norm.
There were several Fraternal Fratenities and Soroities who were Founded under Jewish principles, most were started under Christian principles.
While these two religions were and are predominate there may have been others.
But in this day of Homogonizng, there is inter mingling of thoughts, races, and Ideals.
This is what Greek Organizatios can be in the fore front of doing.