I've been reading over the site.
I believe the name of the order to be the Order of the Knights of Saint George. They were founded in 1390 by Philibert de Mollans, and "approved" (?) by Pope Innocent VIII in 1485.
The requirements for admission are many. This is a Christian order, to start with. The Christian faith is central to the beliefs and spirit of the order.
It appears that at least for certain ranks in the order, having nobility (?) in your paternal ancestry no farther back than your grandfather is a requirement. It also states, "The members of the Order must hold in society a rank compatible with the membership of a knightly Order of traditional prestige." So I gather membership is generally open to what remains of the world's aristocracy (as nationality is not considered for membership) - although "aristocracy" does not exist as such in most of the US (political families aside) it is still alive and well in the rest of the world. It becomes clear that St. George's Knights are truly a traditional knightly order with a long history.
I do not know what would be included in "mutual assistance" - it seems clear that most of the membership of the Eqvites Ivbalis is far from being eligible for membership in St. George's Knights - but certainly we could agree to help each other when in need, should our lack of a religious basis and traditional noble background not be a hindering factor.
I only just now was able to make a quick perusal of the page - let me know if there's any information more specific that you need.
-Christopher Battey, CI