Doesn't Jesus' example in John 13:14-15 give us a standard for communion that includes washing feet?
The only aspects of the communion observance which are mandated are those recorded in 1 Corinthians 11:23-29:
Given Paul's teaching in this passage, the church has very little liberty to alter the celebration, including by adding the washing of feet. Notice in v.23 Paul says he delivered specifically what Jesus wanted the Church to practice, which Paul then outlines in the verses that follow. Foot-washing is not found in that prescription, so we should not include it either.
Obviously, repeating Jesus' foot-washing moment is not wrong, but that does not mean we should incorporate it into the regular pratices of communion. Similarly, Jesus said and did many things that night in the Upper Room, yet we should not attempt to mimic that entire evening as part of communion. We merely repeat the parts Jesus instructed us to repeat. Therefore, in the case of washing feet prior to taking communion, this practice is not prescribed for the Church in Scripture.
Moreover, John 13:14-15 is not an appropriate proof text for defending such a mandate. Washing feet was a practice of that day related to traveling by foot on dirt roads. Prior to every meal, it was customary for the host of the home to have the feet of guests washed by a servant, but Jesus surprises His disciples by assuming the posture of a servant to them. He does this to make a point. Jesus used the moment of washing feet in John 13 to illustrate a larger point that His disciples must maintain a servant attitude of humility.
Notice in v.15 Jesus called that moment "an example," and examples are given to illustrate larger principles. Jesus calls us to follow the principle behind the example, not merely the specific illustration itself. Therefore, Jesus wasn't commanding us to repeat the ritual of feet washing; He commanded us to maintain an attitude of humility with one another which was exemplified by the ritual.
So if a church practices feet-washing as a remembrance of the moment Jesus served His disciples, this is not wrong, however, if a church mandates this practice as part of the communion observance, they go beyond the boundaries of Scripture and misinterpret Scripture.