In Matthew 18:18-20, how does the authority to bind and loose relate to Catholics and non-Catholics?

Verses 17 and 18 are talking about the authority of the Church. The word 'church' is used in verse 17: if your brother sins against you and will not listen to you, you take it to the church, and if he will not hear the church, let him be to you as a heathen and a publican. Then Jesus says, 'Amen, I say to you, whatever you shall bind upon earth shall be bound in heaven, and whatever you shall loose upon earth shall be loosed in heaven.' That applies to the Church, not to you as an individual. Many people get confused here: because the man would not listen to the church, they assume the church has dropped out of the discussion, but the church is still there, and the 'you' in 'whatever you shall bind' is plural in the Greek, referring to all the apostles in the Church. This relates to both Catholics and non-Catholics, because even for non-Catholics the ultimate decision-maker is the church; they simply do not have a pope as the ultimate decision-maker within the church itself. That is the big difference between Catholics and, at least, the mainline Protestant denominations.