Laudator Temporis Acti

Before engaging in religious activities, one should be washed clean. After the Offertory, the priest washes his hands while reciting "Lavabo inter innocentes manus meas" ("I will wash my hands among the innocent") from Psalm 25(26).6 ff. Only those who have been baptized (dipped in water) are entitled to eat Christ's flesh and drink His blood. During Mass on Palm Sunday, the priest walks up and down the aisles, dips a palm frond in an aspersory carried by an altar server, and sprinkles the congregants with holy water. Just inside the doors of churches are stoups of holy water, so that entering worshippers can dip their fingers and make the Sign of the Cross.

There are of course Jewish analogues for these actions, but there are also similarities in ancient Greek religious practices. Among the numerous examples of washing before performing sacrifice, pouring libations, or saying prayers are these:

• Homer, Iliad 1.447-449 (tr. Richmond Lattimore): And the men arranged the sacred hecatomb for the god in orderly fashion around the strong-founded altar. Next they washed their hands.
  
• Homer, Iliad 6.266-267 (tr. Richmond Lattimore): With hands unwashed I would take shame to pour the glittering wine to Zeus.
  
• Homer, Iliad 9.171-172 (tr. Richmond Lattimore): Bring also water for their hands, and bid them keep words of good omen, so we may pray to Zeus, son of Kronos, if he will have pity.
  
• Hesiod, Works and Days 724-726 (tr. Hugh G. Evelyn-White): Never pour a libation of sparkling wine to Zeus after dawn with unwashen hands, nor to others of the deathless gods; else they do not hear your prayers but spit them back.
  
• Euripides, Electra 790-796 (tr. David Kovacs): When we were inside the house, he said, "Someone quickly bring purifying water for the guests so that they may stand around the altar next to the lustral basins." But Orestes said, "We have but recently been cleansed by a pure bath in the running streams of a river. So if it is right for strangers to help citizens at a sacrifice, Aegistheus, we are ready and do not refuse, my lord."

For washing before entering a sacred space, see e.g.:

• Herodotus 2.64.1 (tr. George Rawlinson): The Egyptians first made it a point of religion to have no converse with women in the sacred places, and not to enter them without washing, after such converse. Almost all other nations, except the Greeks and the Egyptians, act differently.
  
• Hippocrates, On the Sacred Disease (tr. Francis Adams): And we mark out the boundaries of the temples and the groves of the gods, so that no one may pass them unless he be pure, and when we enter them we are sprinkled with holy water, not as being polluted, but as laying aside any other pollution which we formerly had.