I know this is a practice in some more recent Protestant traditions. But am unfamiliar with it as a traditional practice.
The Eastern Orthodox and Oriental Orthodox do it, to a limited extent, on Maundy Thursday, and it used to be de rigeur in the West, with royalty washing the feet of commoners, and later giving them coins in lieu of washing their feet, which is still done in the UK to this day.
It is normal for the foot washing to be the washing by one in a position of leadership of those in a position of lesser or no authority. In the Syriac Orthodox Church (and I believe in the Armenian and Coptic churches), the bishop will wash the feet of the boys who serve as Psaltis in the altar, who are the junior-most clergy, having not yet earned the stole of a reader, and having no authority; therefore it is meet that their feet should be washed by the bishop, who has the most authority, yet who is normally elderly and who can only bend down to wash their feet with great personal discomfort and difficulty in most cases.
I prefer this to the Eastern Orthodox liturgical practice, which is also beautiful, but not to the same extent, where presbyters will wash each others’ feet in a mutual manner if there is a concelebration on Holy Thursday. I regard the liturgy of the Oriental Orthodox and Eastern Orthodox as equivalent in beauty overall; in some cases, I think some of the churches or one particular church does a particularly good job at something or has preserved something that has fallen out of use in some or all of the others (such as the Presanctified Liturgy, which used to be celebrated in all ancient churches, but has been disappearing from various rites, or the Cathedral Office, which was replaced entirely by the Monastic Office in all churches except the Assyrian Church of the East and to a lesser extent the Roman Catholic Church, and which was partially preserved in the Coptic Orthodox Church in the form of the Morning and Evening Raising of Incense (the Coptic Orthodox Divine Office or Liturgy of the Hours is derived from three quite different sources, so in addition to the aforementioned, there are also the Hours of the Agpeya, which is the recitation of most of the Psalter throughout the day, and the Psalmody, which is basically a combination of Vespers, the Midnight Office and Matins, but its division into three units spread out across evening, midnight and the early morning before dawn mirrors the Midnight Office being divided into three watches as in other liturgies. Another example would be the service of Holy Unction, where the Byzantine and Coptic Orthodox, who use basically the same liturgy, have the most beautiful service for the anointing of the sick and the fasting with oil, consisting of seven sets of prayers and Scripture lessons during which the oil is consecrated (and pre-consecrated oil is available for use throughout the year, although the Eastern Orthodox prefer to celebrate the liturgy of the consecration, with seven priests if possible, or six priests and a bishop, in the house of a sick person or in the church if the sick person can get there, which I like).
However, it is not a tradition in any ancient church for all of the laity to wash each other’s feet every time they participate in Holy Communion. The coupling of the two events liturgically by the Adventists is something I strongly disagree with, because the washing of feet was a different event which happened shortly before the Last Supper but was not part of the same thing, and which also occurred in the same time that St. Mary of Bethany washed the feet of Christ our True God with perfumes from an alabaster box, to the ire of Judas Iscariot, and another woman, probably St. Mary Magdalene, washed His feet in her tears.
So there was a great deal of foot washing going on, and it was an important and loving act, but we are not required to do it insofar as it is not an ordinance, but it is a nice touch for Holy Week and does have a long history of being done in the Anglican and pre-Anglican British Catholic tradition and in the Eastern and Oriental churches (I think the Assyrian Church of the East does it also, but am not sure; I will ask my friend).
