Objection #1: The text says "anyone." That means anyone! It can't get clearer than that!
Of course, this is falling under the trap of branching a word out from its immediate context. For example, when our Lord tells His disciples "If you ask Me anything in My name, I will do it" (John 14:14), does He literally mean anything? So if I wanted to rob a bank, He would help make it happen? If I want to ask God to kill someone's child because I don't like kids, is God going to do it simply because I asked? Could we honestly say that anything means literally anything within the full context of this verse? Of course not.
Let me give a parable to explain this point further. Suppose there is a man who gets a job on a military base, and works at a building with tighter security than most buildings on the post. You need an identification and special key card to get inside, and human guards have to approve you to let you in. If you have neither cards and the guards don't recognize you, you can't get in. Now imagine there's a food court for employees inside the building. A newly hired employee gets in and, seeing the food court, is unsure if anyone can eat there, or if it's only for special people. A fellow employee tells him, "Oh, don't worry, anyone can eat there." The newly hired employee is happy, and later tells a friend about it. The friend, hearing the words "anyone can eat there," decides he wants to eat at the food court too. So he goes to the building and, upon walking in, is promptly rejected by the guards. Flabbergasted, the friend declares, "But I was told anyone can eat at the food court!"
Of course, the friend's dilemma is exactly the same dilemma as those who do not understand why "anyone" in Revelation 3:20 can't literally apply to anyone in the world: context, context, context. The new hired employee had meant that anyone among the employees could eat at the food court. Likewise, Christ is referring to anyone within the church who answers the knocking at the door.
Objection #2: You can't say it's prophetic language when it's spoken of in the present tense. Christ is knocking in the here and now and expecting and answer.
Christ does indeed speak of knocking on the door in the present tense, rather than speaking in the future tense as he does elsewhere in the previous chapters. However, only the action is in the present tense, whereas the desired response has yet to be initiated. If Christ were speaking in our modern tongue, He might say, "All right, I've made the move - the ball's in your court now." This response would, of course, be in a future tense.
Also to be taken into consideration is that the result of the decision (the entering of Christ and the dining together) speaks of the supper of the lamb, which throughout all of scripture is always in reference to the day of judgment and the blessing of the saints with eternal life. This is a future event. Both the verbs "come in" and "dine" are future tense verbs in the original Greek.
Objection #3: This doesn't have any similarity with other judgment passages regarding the second coming, so you can't possibly compare it to the "master returning" parables told by the Lord in the gospels.
On the contrary, we find a great similarity in Luke's gospel:
"Be dressed in readiness, and keep your lamps lit. Be like men who are waiting for their master when he returns from the wedding feast, so that they may immediately open the door to him when he comes and knocks. Blessed are those slaves whom the master will find on the alert when he comes; truly I say to you, that he will gird himself to serve, and have them recline at the table, and will come up and wait on them. Whether he comes in the second watch, or even in the third, and finds them so, blessed are those slaves." [Luke 12:35-38; NASB]In fact, I had cited this verse in my original post, although it seems to have either been ignored or not checked carefully.
Objection #4: Why can't it mean anyone other than believers?
Because that is not the real context. If you want to quote this verse in a different context but using similar language, very well - but you can't make the claim that this is what the text actually says, because that would be simply erroneous. Christ is not addressing those outside the church, but those within the church.