Rhiannon's reply is roughly what mine would be to that point....your own point that "it is a religion still in practice".. justifies The Wailing Wall being used as it is...
As no-one really knows the exact religion of the people who put stones where they are, so the leaving of offerings is for peoples' own benefits(I daresay there are people who go to modern churches and make a show of putting a generous wad in the collection plate, as if to say, "My offering is bigger than yours!"..strikes me as being like leaving a physical offering by a site ..pointless..if you consider the site spiritual)...and to repeat the oft-made point, these days people are just adapting the sites for their own purposes...even to the extent of laying claims to be following an ancient religion of which there is no evidence for. Even the Druids came long after the erection of many of these sites, and perhaps the pre-romanic druids did use them for their own benefit(much as the church did after them)..but again as to this we only have romanic propaganda against the druids as any kind of evidence...so it isn't an accurate portrayal.