The best I can tell they try to stay neutral and don’t stay strictly on one side or the other.
The only time I visited the museum was brief. Robert Gordon was stationed out front of the building looking rather discouraged. But dealing with the folks there via the net and watching quite a few videos and the way they handle questions, etc leads me to believe that they don’t take one side or the other.
I would have to agree with Jerry on this one. The museum has to present the evidence not speculation. I am not saying they should say that the Warren Commission is unassailable but they should point out that it took into account a great deal of evidence that has withstood the test of time.
The conclusion that Oswald shot JFK and that he acted alone is evidence based. Conspiracies aren't. The entire record does not contain a scintilla of evidence of a conspiracy. There is abundant evidence that Oswald was involved and no evidence that anyone helped him or plotted with him. While the possibility of a conspiracy cannot be absolutely excluded, the evidence demonstrates that it would be highly unlikely that Oswald would have been selected as the person to carry it out.
What the museum can and should do, however, is recognize that there is some controversy over the Warren Commission conclusions and to show the variety of all the mutually exclusive conspiracy theories that have cropped up over the years. If nothing else, it would make the museum entertaining. What the museum must not do is suggest that these theories have any evidentiary basis - unless they actually present the evidence. I think trying to do that would be a huge waste of museum funds.