In this link from Zenit, it is stated it is the role of the priest to wash the feet of men on Holy Thursday.
The rubrics for Holy Thursday clearly state that the priest washes the feet of men (“viri”) in order to recall Christ’s action toward his apostles. Any modification of this rite would require permission from the Holy See.
It is certainly true that in Christ there is neither male nor female and that all disciples are equal before the Lord. But this reality need not be expressed in every rite, especially one that is so tied up to the concrete historical circumstances of the Last Supper.
A-3: The rite of the washing of feet is not obligatory and may be legitimately omitted. However, this is usually not pastorally advisable.
While the rite may not be delegated to a non-priest, a concelebrant may substitute the main celebrant for a good reason.
zenit.org/english/visualizza.phtml?sid=51112