(1) I strongly suspect that this question takes a decidedly unorthodox position on the anthropic principle. Normally, the anthropic principle has nothing to say about how many cilizations exist, only that the universe is fine tuned for civilizations to exist. (2) However large the observable universe is, it is still finite. As a consequence, at any given moment in Earth time there are a finite number of civilizations in it. Two is a number as any other, so that there is a finite greater than zero probability that right now the number of civilizations is two.

Worldbuilding is about the infrastructure of the world/universe. Worldbuilding rules are true regardless any story. You don't appear to be asking for help solving a worldbuilding problem because neither hypothesis you mention reflects a known and proven rule of the Real Universe. In short, VTC:Too Story-Based because you're asking us to create a fictional hypothesis, building upon the other two, that "explains" a rule you've already set in your universe. Per the help center, we don't help write your story.

I’m voting to close this question because the answer is trivially "the story requires it", since there is no reason there can't be just two civilizations. Not quite Story-Based, because you're not asking about the story, but you are asking about something that a) science cannot possibly explain and b) will automatically be true if the story needs it.

Question: Are we allowed to have multiple sentient Civilizations... that died out - Whether by natural means or unnatural - or must it be only 2 ever. Also, are we allowed non-sentient life?

@JBH I don't understand your VTC. There is no reason that any hypothesis should have to reflect a known and proven rule in the Real Universe in order to be true in a fictional setting. Each hypothesis is just a rule for his setting. This question is simply asking for some third rule or explanation that allows both of these hypotheses to be true at the same time which is a textbook WorldBuilding question.

@controlgroup You are missing that the OP is positing that The Copernican Principle and the Anthropic Principle are both facts in his setting. Once you make the assertion that a principle is true in your setting, you can no longer just say because "the story requires it" without breaking your setting's internal consistency. You need to be able to explain what makes it internally consistent.

@Nosajimiki: You are missing that the Copernican principle and the Anthropic principle have no bearing on the number of civilizations which can exist simultaneously in the observable universe.

@Nosajimiki My VTC is based on what appears to be the request to create a work of fiction (a fictional document). The OP has already set the rule (only two civilizations), now he/she is looking for the narrative necessity to rationalize them. Not our job. (The fact that the linked hypotheses don't reflect known facts simply underscores how fictional this document is.) This, in addition to Alex's comment.

@Nosajimiki One more thing, a comment to your comment to ControlGroup. The OP has not asked us to accept the two principles as facts in his/her universe. The OP is assuming they're facts in the Real Universe. And I disagree that an explanation is required to be internally consistent. It's like saying "Nations X and Y are at peace, why?" That's storybuilding. The fact they're at peace is the world rule. Explaining it is the story.

This is a perfect question for the Story Tellers Corner chat room, where anything can be asked.

@TheDemonLord - Yes this is acceptable - as long as there is only '2' in the universe at one time.

@JBH I understand what you're saying, but at the moment in my world we are talking about consciousness and the universal principles of science. It is impossible to develop a 'story' without first outlining how indeed (or a likely cause, or at least a framework that allows) there to be only 2 civilisations.

@controlgroup ha ha - sure 'because the story requires it' can eliminate any question:) But I find that unsatisfactory due to characters in the story are intelligent smart and scientifically motivated, and this weird 'how is it possible that there are only 2 of us' is the white elephant in the room behind every conversation they have, and given they already have thoroughly discussed the two principles (in terms of consciousness and in terms of scientific universality).

@JBH - Apologies - the characters have already had in depth discussions and knowledge about both principles - I will edit the question to add this as a parameter for you.

@AlexP Yes - I agree. The reason why the 'bonus' part of my question is there is that I would like not only the answer to be possible, but 'likely'. I find it unsatisfactory (the characters do, as do I the writer, as does the reader) that an arbitrary number, so close to 1 but not exactly 1, is the outcome from these two principles.

What a delightful question! This is much better than the usual run of orbital mechanics. My only quibble is that you might misapplying the Copernican Principal to something that doesn't actually rely on the Principal to happen. That article has some interesting errors, but it seems that the CP refers solely to physical location, not what's living on the planet. How will you rectify that?

The problem with this question is that you're asking us to brainstorm and generate ideas for you. That is prohibited on this site. Around an unremarkable star in your world orbits the anthropic teapot. Except for the fact that it is a mcguffin it's perfectly ordinary in every way. As long as the teapot exists your universe, through no mechanism that exists within it, your universe shall always have EXACTLY two sapient, sentient, civilizations. As for the mechanism, there exists a mcguffin. How that mcguffin works doesn't matter.

@elemtilas Thanks - I do prefer world building around concepts of philosophy, especially exploring ideas where consciousness, meaning and culture intersect science, realism and mundanity. In this case I take your point - CP is that we are not in a special location, not necessarily that we are not unique. However - If we do encounter 'many' other alien civilisations that confirms that we are not really in a special location (ie. the 'heart' of the CP)- My question really relates to a conundrum where if only one is encountered, and the rest of the universe is void and empty: how is CP preserved?

@sphennings Hmmmm - what do you think though? If you were reading my story would you not think that something was not internally consistent and scream out 'Why?'. If you don't - I suppose that's ok, but I'm really trying to lay the 'ground work' for a setting where these principles are reconciled. I'm not really asking for brainstorming, I'm more asking for expertise on the way forward for both principles to be true, and also allow for only two civilisations. I don't think that's opinion - this is straight territory of good reasoning (the edge of perception & science) that WB SE is all about.

@AlexP I'm not forgetting that it can be, only acknowledging the improbability of it. Saying there can be 2 and only 2 sentient species that evolved space tech at about the same time in the whole universe is like saying you can crack an RSA-256 encryption key on your first try... past a certain point, improbability needs to be explained to maintain a suspension of disbelief.

@JBH The OP expressly states "The solution must comply with both the Copernican and the Anthropic Principles." That makes these statements of fact in his setting.

@sphennings the "Brainstorming" restriction refers to questions that ask for an exhaustive list of ideas. The OP is only asking for one explanation and has done a good job defining what a best possible answer should like which is the proper protocol for questions that could reasonably have a lot of possible answers.

I concur with Nosajamiki on the brainstorming question. This query doesn't strike me as the OP asking us an open ended request for a huge list of ideas.

Also concur with the two Principals being essential rules of the world.