I don't really have that much trouble with massed priests. I will add that priests will usually mass in Classical in most of my games. (Strange...)
Several people sometimes are deluded into massing several priests as you can get them in Archaic and not many other civs can mass something military wise. May I remind all those people that you're wasting gold that can be used on something better. People think taht since you don't need Gold to advance to Classical 'I can get it free'. I doubt you need MASSED priests unless you're against a MU spammer, or if you're Ra. Still, as Ra, you will only need 2 more than the usual to empower your resources (Pharoah on either Food/Gold).
I have met quiet a few players who massed priests and I countered them fairly easily.
I was Norse, Odin. 2v2. He was Isis. I sent my ulf to build a forward base to rush this guy as I can mostly am able to rush in the early hours of Archaic (By this I mean get a few units out in my early Classical whilst the enemy is still in Archaic usually).
I end up buidling three longhouses. I have chosen Heimdall, so I decide to get some units coming. I get about 2 or 3 RCS out and raid his Gold Miners nearby and they leave. Then a few short minutes later, he comes back with massed priests. For some strange reason he mananged to kill my 3 RCs though i mananged to kill 1 or 2 of his priests. However, he instanly replaces the lost ones and pursues my 4th RC, He discovers my Forward Base and sends his priests to attack one of the buildings. I really don't know whay he did it. This gave me time to que up TAs, Ulfs & a few more RCs to a place he couldn't see. When I had enough forces, I sent them to attack the priests ( he asummed I had abandoned my base). All died within a few seconds. I understand many will say why make TA, Ulfs when they have loe pierce armour? I can safely say that I had wood not going to use (I tasked my new units to build 2 more longhouses then used wood to build TAs). I built Ulfs cause they are to fast for the priests and are supported by the other two units, they also have a decent attack and are quick to build.
I was then able to take on his TC. I dunno why. I wanted revenge. I got it. I used Undermine on his TC. My Einharjar didi a great job boosting my unit's attack. About a third of my army died so i replaced them, though not fast enough. Eventually the TC crumbled leaving me 2 RCs, 4 TA & 3 Ulfs & 1 Einharjar.