Foxnews reports on a petition that is being circulated by the Campaign to Defend the Constitution. The petition itself can be found here. This takes the form of a call for Answers in Genesis, the group that Ken Ham is connected with, to "cease their war on science and we call on educators, media, and citizens to exercise critical thinking", rather than a boycott or any sort of demand to have the museum closed. So, in that sense, it is not anti first amendment. Having said that, it clearly is not a constitutional issue and its placement on their page is somewhat peculiar. It would seem that they are reacting to statements like this by Ken Ham:
"We use the same science they do...What they're really saying is they disagree with our beliefs about history, about the Bible, but we use the same science and genetics they do."
Even if you have had your head in the sand for the last hundred years, you know this simply isn't so. As Henry Morris once said:
"No geological difficulties, real or imagined, can be allowed to take precedence over the clear statements and necessary inferences of Scripture."1
There is clearly a need to interpret palaeogeological and palaeontological data within a scriptural framework. Therefore, creationism proceeds deductively--with a fixed conclusion. This is antithetical to science, which has no fixed conclusions. Ken Ham knows this. His response is nothing more than smoke and mirrors.
The problem that I see is that if children go to this museum and believe what they see and hear, and then grow up learning about mainstream scientific approaches to the data, most if not all of them will say to themselves, "what a bunch of hooey!" and reject Christianity altogether. I fear that little good can come of this.
1Biblical Cosmology, page 33