The Wanderer: Schneider made a clear statement about this matter, as follows:
“As concretely to the innovation of washing the feet of women during the Holy Mass of the Last Supper on Holy Thursday: This Holy Mass celebrates the commemoration of the institution of the Sacraments of the Eucharist and [of] the Priesthood. Therefore, the foot washing of women along with the men not only distracts from the main focus on Eucharist and on Priesthood, but generates confusion regarding the historical symbolism of the ‘twelve’ and of the apostles being of [the] male sex….
“By the way: The public washing and usually also kissing of the feet of women on the part of a man, in our case, of a priest or a bishop, is considered by every person of common sense in all cultures as being improper and even indecent. Thanks be to God, no priest or bishop is obliged to wash publicly the feet of women on Holy Thursday, for there is no binding norm for it, and the foot washing itself is only facultative.” Full report, with input from Cardinal Sarah here.