The rubrics do state that “select men” are to be used for the ceremony of the washing of the feet; however, “men” could include women if we take into account the Latin “mens” which basically means “a thinking human being.”  There is also the, “Jesus washed the Apostle’s feet and they were male” idea as well.  So what do we do?

Well, the washing of the feet is not a sacrament, nor does it open the door to Holy Orders for those participating in it.  Here is what the USCCB has to say:

The rubric for Holy Thursday, under the title WASHING OF FEET, reads:

“Depending on pastoral circumstance, the washing of feet follows the homily. The men who have been chosen (viri selecti) are led by the ministers to chairs prepared at a suitable place. Then the priest (removing his chasuble if necessary) goes to each man. With the help of the ministers he pours water over each one’s feet and dries them.”

Regarding the phrase viri selecti, the Chairman of the Bishops Committee on the Liturgy, after a review of the matter by the committee, authorized the following response which appeared in theBCL Newsletter of February 1987:

Question: What is the significance of the Holy Thursday foot washing rite?

Response:

1. The Lord Jesus washed the feet of his disciples at the Last Supper as a sign of the new commandment that Christians should love one another: “Such as my love has been for you, so must your love be for each other. This is how all will know you for my disciples: by your love for one another” (see John 13, 34-35). For centuries the Church has imitated the Lord through the ritual enactment of the new commandment of Jesus Christ in the washing of feet on Holy Thursday.
2. Although the practice had fallen into disuse for a long time in parish celebrations, it was restored in 1955 by Pope Pius XII as a part of the general reform of Holy Week. At that time the traditional significance of the rite of foot washing was stated by the Sacred Congregation of Rites in the following words: “Where the washing of feet, to show the Lord’s commandment about fraternal charity, is performed in a Church according to the rubrics of the restored Ordo of Holy Week, the faithful should be instructed on the profound meaning of this sacred rite and should be taught that it is only proper that they should abound in works of Christian charity on this day.”¹
3. The principal and traditional meaning of the Holy Thursday mandatum, as underscored by the decree of the Congregation, is the biblical injunction of Christian charity: Christ’s disciples are to love one another. For this reason, the priest who presides at the Holy Thursday liturgy portrays the biblical scene of the gospel by washing the feet of some of the faithful.
4. Because the gospel of the mandatum read on Holy Thursday also depicts Jesus as the “Teacher and Lord” who humbly serves his disciples by performing this extraordinary gesture which goes beyond the laws of hospitality,² the element of humble service has accentuated the celebration of the foot washing rite in the United States over the last decade or more. In this regard, it has become customary in many places to invite both men and women to be participants in this rite in recognition of the service that should be given by all the faithful to the Church and to the world. Thus, in the United States, a variation in the rite developed in which not only charity is signified but also humble service.
5. While this variation may differ from the rubric of the Sacramentary which mentions only men (“viri selecti”), it may nevertheless be said that the intention to emphasize service along with charity in the celebration of the rite is an understandable way of accentuating the evangelical command of the Lord, “who came to serve and not to be served,” that all members of the Church must serve one another in love.
6. The liturgy is always an act of ecclesial unity and Christian charity, of which the Holy Thursday foot washing rite is an eminent sign. All should obey the Lord’s new commandment to love one another with an abundance of love, especially at this most sacred time of the liturgical year when the Lord’s passion, death, and resurrection are remembered and celebrated in the powerful rites of the Triduum.^{3  –}http://old.usccb.org/liturgy/q&a/general/feet.shtml

This basically leaves it up to the pastor to decide how to carry on the service of the washing of the feet. Apologist Jimmy Akin wrote an excellent explanation here which is worth reading:

I feel that this is a whole lot about nothing.  I understand some people’s need to have literal visuals that bring to life the Gospel, but what’s important is that we internalize the action of the washing of the feet.  Jesus did this to show service and charity.  The washing of the feet was not meant to be some initiation ritual for an all men’s club.  Jesus washed the feet of the 12 to show that He has come to serve not to be served (Matthew 20:28).

Think about it.  Do we really need to act out a play similar to Mel Gibson’s “The Passion of the Christ” on Good Friday with the gore and blood?  Is this really necessary in order to be “faithful” to the Gospel? 

The reality is that via these visuals we must internalize the message.  Whoever are chosen to be part of the service of the washing of feet does not matter.  It is the message behind this service that does.  To my knowledge, the rubrics do not state that the “select men” must be Catholic.  Pope Francis by washing the feet of a Muslim is showing true service that reaches all.  Christ welcomes all and served all while He walked the Earth. 

Pope Francis as Pope holds complete authority over the Church including Canon Law and the Rubrics of the Church.  Remember, Peter has the keys to bind and unbind! 

Fr. Longenecker puts it correctly, he writes on his blog: “In the gospel Jesus repeatedly flouted some strict rules for a greater good, and so upset the religious legalists. Did the Pope break the rubrics? At the end of the day the rubrics are there to serve the gospel–not the gospel to serve the rubrics.”