According to Evangelicals, who now has the authority to bind and loose (per Matt. 18:18)?

You may possibly misreading the Scriptures. As I read the whole of chapter 18, I come away with a much different impression. Did Jesus give the authority only to the Apostles?

Matthew 18:16 and 17 KJV But if he will not hear thee, then take with thee one or two more, that in the mouth of two or three witnesses every word may be established. 17 And if he shall neglect to hear them, tell it unto the church: but if he neglect to hear the church, let him be unto thee as an heathen man and a publican.

Jesus to my mind gave that authority to the Church (all believers as a group). And his reason for doing so appears to be:

Matthew 18:20 KJV For where two or three are gathered together in my name, there am I in the midst of them.

This authority appears to be a shared authority there am I in the midst of them presumably any decision made by the group would be influenced by Jesus who is in their midst. And if we consider both verses 18 and 19 together

Matthew 18:18 KJV Verily I say unto you, Whatsoever ye shall bind on earth shall be bound in heaven: and whatsoever ye shall loose on earth shall be loosed in heaven. 19 Again I say unto you, That if two of you shall agree on earth as touching any thing that they shall ask, it shall be done for them of my Father which is in heaven.

it appears that those decisions have eternal consequences since it is God himself taking the action.

For those and many other reasons we as members of the Church (not Denominations) must be very careful in our agreed stances since as little as two of us can have eternal effects on another.

This interpretation of these Scriptures is also shared by Peter Guzik.

Relating to one another in the Kingdom Community. 1. (15) If you are sinned against, go and confront the guilty party directly. "Moreover if your brother sins against you, go and tell him his fault between you and him alone. If he hears you, you have gained your brother." a. Go and tell him his fault between you and him alone: It is essential that we go to the offending brother first - not griping and gossiping to others, especially under the guise of "sharing a prayer request" or "seeking counsel." Instead, speak to the party directly. i. It would be wrong for anyone to take Jesus' word here as a command to confront your brother with every sin they commit against you. The Bible says we should b. If he hears you, you have gained your brother: You have gained him in two ways. First, the problem has been cleared up. Perhaps you realized that he was right in some ways and he realized you were right in some ways, but the problem is resolved. Second, you have gained him because you have not wronged your brother by going to others with gossip and half the side of a dispute. 2. (16-18) If one among the church is adamantly unrepentant, they are to be removed from fellowship. "But if he will not hear, take with you one or two more, that 'by the mouth of two or three witnesses every word may be established.' And if he refuses to hear them, tell it to the church. But if he refuses even to hear the church, let him be to you like a heathen and a tax collector. Assuredly, I say to you, whatever you bind on earth will be bound in heaven, and whatever you loose on earth will be loosed in heaven." a. If he will not hear, take with you one or two more: The circle of people in the situation only becomes wider as the offending party refuses to listen. If the stubborn, unrepentant attitude remains they are to be refused fellowship (let him be to you like a heathen). i. This sense of being refused full standing and participation in the body of Christ is what Paul meant when he said to deliver such a one to Satan (1Co. 5:1-8). There is a sense in which the unrepentant one is chastened by their being placed outside of the "protection" of fellowship. b. Like a heathen and a tax collector: Even so, the unrepentant one must be treated just as we should treat a heathen and a tax collector - with great love, with the goal of bringing about a full repentance and reconciliation. c. Whatever you bind on earth will be bound in heaven: If this process is done humbly and according to the Word, this is quite binding in the eyes of God, even if the unrepentant ones just go to another church. 3. (19-20) The power and blessing in fellowship that is denied the unrepentant. "Again I say to you that if two of you agree on earth concerning anything that they ask, it will be done for them by My Father in heaven. For where two or three are gathered together in My name, I am there in the midst of them." a. If two of you agree on earth: There is real power in agreement in prayer and in the presence of Jesus. This is exactly what the unrepentant ones miss out on. i. In the ancient Greek, agree is literally "to symphonize." Jesus wants us to complement each other like a great orchestra. b. It will be done for them by My Father in heaven: We must take advantage of the power of agreement, which works on the principle related in Deu. 32:30, where one sets a thousand enemies to flight, but two set ten thousand enemies to flight. There is real power the prayer of agreement. c. Where two or three are gathered together in My name: Gathering in the name of Jesus means gathering according to His character and will, and gathering in a manner Jesus would endorse. This is when Jesus is really present (I am there in the midst of them).

Certainly many will look at my answer with a jaundiced eye, but after much study of the Bible this is more in keeping with my impressions of Jesus and his administration of his Church. It seems to me that Jesus would not want this authority to pass away with the Apostles and that seems to be the underlying reason for the Catholic Church having Papal descended. Whether the Catholic Church or my interpretation is correct that authority did not pass away, and depending upon which is correct the answer to who has that authority today appears to be either the Pope or the Church, or maybe both.

Has my answer left you in a more confused state than before?

Hope this helps.