“different scientists can reach very different conclusions, depending on their starting assumptions.”
The sentence is correct, but it does not prove the point the creation museum wants to imply.
What exactly is science and a scientific approach ? While there are many, many explanations,
I think the most succinct explanation is that science tries to get information about something where people from different cultures and worldviews can agree to get the most accurate representation of the known observations together.
Let's say what that means if you are a scientist and you are investigating a tyrannosaur skeleton. What do you write in your observation book ?
"Found an incomplete skeleton at location XYZ. Started excavation at
the timepoint XYZ and ended XYZ. Skeleton consists of X parts, please
see the excavation map where the parts have been found and the photo
page for each fossilized bone found. Strata seems to be in the
Santonium epoch, I appended a sample for further observation. Tibia bone has
severe fracture."
What this description shows is that it can be read, understood and accepted by everyone, both cavemen and scientists of the 25th century (Well, the Santonium epoch must be explained further, but it can be done). The scientist tells only the observations he/she made. Now he/she can make further statements:
The fracture seems to be relatively fresh, perhaps shortly before its death. I think it
is probable that it was wounded, retreated to this position and starved.
This may trigger disagreement. The caveman looks at the location (it is geologically stable, so not much change) and says that a wounded animal would never choose such an exposed position. Another scientist says that he excavated many fossils and in his experience the fracture is not fresh. The 25th century scientist may shake his head and point out that the bone has been reexamined with XYZ technology and found to be fractured 2,5 years before the demise of the tyrannosaur.
What is important is that everyone has in fact different experiences and they are arguing from their point of view. There is nothing wrong about it, each other can talk and argue together.
The concept is "methodological naturalism". It may be that you have deep inner convictions,
are Christ, Buddhist, Muslim etc., but if you discuss scientific questions, you stick to the things which all participants accept. You do not try to find solutions which does not explain anything ("If I cannot explain that, I introduce God/demon/whatever").
That the dinosaurs are 4000 years old because your Bible says so is not a valid argument because a Buddhist does not believe in a Bible. But both can agree that there is an excavated bone which looks fractured. This works in reverse, too: If the scientist which wrote the report is a deeply believing Christ, but stick to the facts he/she is a better scientist than a humanitarian atheistic scientist letting his emotions clouding his judgement.
Some misconceptions uttered here:
scientists then check their conclusions against reality, and reject or change their
assumptions if reality and conclusion don't match.
In your dreams. Really, scientists are humans and I am sick that we are painted as defenders of wisdom. Scientists are not better than other people ! They may have pet theories, build groups, hate each other's guts, fight for funds and act irrationally & unfair.
(See the feud "Out of Africa" vs "Multiregionalism" in anthropology).
But it does not mean that scientific work is not done and most scientists could not work together most of the time. But conflicts arise from time to time.
If two scientists disagree about some issue, then at least one of them is wrong. That
is, at least one of them has an idea that does not correspond to how the world works.
Wrong. Wrong. Wrong. Both scientists may be wrong. Both scientists may be partially right.
One scientist may have the correct argumentation, but he/she is still wrong because the data the argumentation depends on is not correct. It may even be that there is not enough data or conflicting data to come to a conclusion, the question may be not resolvable (currently) and a discussion may be pointless. Everything is possible.
ADDITION: I thought the answer to the last question: "What is the best rebuttal against (the philosophical mindset of) this exhibit?" is quite obvious.
If you are someone which is interested to settle the question about a dinosaur skeleton and you never have encountered the Bible the question automatically arises: "Which information has the bible which is relevant to the excavation of the dinosaur skeleton ?" You are asking this question completely neutral and you are genuinely interested.
Does the bible mention dinosaurs ? No. There is a dragon, a leviathan and a behemoth. None of them has realistic properties or is remotely like a dinosaur. No seven heads or several horns, no throat with fire or smoke, no dinosaur capable to hide itself in mud. Apart from that, the descriptions are fantastic, the dragon is throwing stars down.
Given that, is the Bible at least consistent (meaning that it does not contradict itself) ?
No. The bible states that the human came after the animals (Genesis) and two pages later it states that the animals came after the human. Adam and Eva were the only humans and had only two childs: Kain and Abel. How were humans then able to procreate ? In the New Testament the differences between the evangelists are stunning.
Given all that information, every information from the Bible or extracted from the Bible (the 4000 years BC often quoted are the addition of ages which are itself completely exaggerated from a modern viewpoint) is simply not relevant for the examination of the dinosaur skeleton and should never find its way into the discussion. This is a viewpoint which can be understood even by a religious Christian. If he/she can understand that people may come from a completely other culture and never came in contact with the Bible, he must contain the discussion to argumentations which can be shared. This disallows also "leaps of faith" by invoking explanations of indefeasible origins (supernatural, taboo).