My experience of these place-name elements in Orkney inclines me to think they all relate. The tendency has been to see mess- names as meaning mass and referring to churches, as with the Messigate names in St.Andrews. Down in Holm the irregularly shaped hillock of Mass Howe was associated with a known-of chapel site but currently more seen as relating to the many Moss 'marsh' names along this stretch of the parish [the also noted Mass Gate track actually seems to head more to the smaller and more circular hillock above this, and in a certain light I have photographed a vertical strip outlined on the side facing the road to thats left. {Between this and the road above the same day also showed rectangular cropmarks where CANMAP has nothing} ]. The other day I was researching the Hillhead of Crantit above Highland Park Distillery (a walled enclosure on the right as you leave town, the low ruins of a house within) and the 1882 map shows an odd rectangular feature by the road opposite, which (now) relates to Mayfield House. Knowing that this was not in Orkney a reference to hawthorn I thought it worthwhile to find the etymology. Except there isn't one. Nor for any similar names. And despite a few attempts no-one seems to have one for maes- names (most obviously Maes Howe).
So my hypothesis is, given the propensity to place Christian sites upon/by those of pagan veneration, that many of these not specifically church-type placenames are indicators of such prior sites. The question is are there pre-Christian sites outwith Orkney that have Mess/Mass/Maes/May placename-elements attached to them ?