Did they start out as civic fraternal organizations like the modern(ish) grange society? Did they have any known connections to Jacobitism or other external influences? Also, did they were described as wearing white aprons indicate any known connections to Freemasonry?
There has been a lot of debate over these societies in the past and some aspects of them are still understudied. These agrarian societies were predominantly a reaction against economic difficulties, the required tithes to the Church of England, and the political and economic predominance of Protestant landlords. It is important to remember that farming in Ireland was communal for many centuries. The Rundale system ensured that communities farmed a lot of land (especially in the Western half of the island) in common. This meant there were closer ties within the community. This communal outlook fed into the creation of agrarian societies. Such societies were oath-bound, which makes them fraternal to a point, but there was not much drinking and celebrating because these organizations were outlawed. In fact, the Whiteboys oath included a clause stating that they would not drink "while on duty." Their white clothing was mostly so they could identify each other in the dark.
However, recent scholarship has discovered links between Jacobitism and Whiteboyism though the extent of that relationship is not entirely clear. Newspaper reports on Whiteboy meetings stated that they were singing disloyal songs and drinking toasts to Prince Charles Stuart. Part of this may have been due to the fact that Jacobites were absorbed into these new movements.
As far as ties to Freemasonry go, the Protestant societies that opposed agrarian societies became closely tied with Freemasonry with the invention of the Orange Order in 1795. Some Whiteboys and Ribbonmen did get absorbed into the United Irishmen in the 1790s, which brought them more closely in line with Enlightenment ideas and nationalist politics. The United Irishmen definitely had external and international influences. They were in contact with French societies as well as some in the fledgling U.S. These international connections and links with other societies became a widespread pattern in the 19th century.
Sources
Foster, R. F. Modern Ireland, 1600-1972. New York, N.Y.: Penguin Books, 1989.
Kelly, James, and Martyn J. Powell. Clubs and Societies in Eighteenth-Century Ireland. Dublin: Four Courts, 2010.
Ó Ciardha, Éamonn. Ireland and the Jacobite Cause, 1685-1766: A Fatal Attachment. Dublin, Ireland: Four Courts Press, 2002.
Williams, T. Desmond. Secret Societies in Ireland. Dublin: Gill and Macmillan, 1973.