Does this mean that The Ark Encounter in Kentucky, that requires all employees to certify that they are true believers in the Christian god, is illegal under the terms of the US Constitution ?
depends on if the Ark Encounter in Kentucky was part of Congress. Here is an example. Marijuana usages could have allusions to religion and the moralities of religion, per se. Congress, as part of Federal, holds marijuana as 'not legal' on the Federal level. But each State can choose to have their own 'legalities' towards marijuana. Congress did not pass these State laws because they still hold marijuana as 'illegal' but they do not infringe upon the rights of States to have marijuana 'legal' in their States.
The same applies to same sex marriage. Congress did not pass a law that says same sex marriage needs to be honored in each State. They left that up to each individual State. However, for those States that do want to recognize same sex marriage rights and obligations, they are entitled to and free to. They might even be able to change 'marital' obligations if they wanted to.
The First Amendment (Amendment I) to the United States Constitution prevents Congress from making any law respecting an establishment of religion, prohibiting the free exercise of religion, or abridging the freedom of speech, the freedom of the press, the right to peaceably assemble, or to petition for a governmental redress of grievances.
Congress did not make any law respecting nor disrespecting of any establishment of religion, prohibiting the free exercise of religion or abridging of freedom of speech, or abridging the freedom of the press, or abridging the right to peaceably assemble, or abridging the petition for a government redress of grievances.
I guess, in a nut shell, each State is somewhat semi-autonomous but still under National Welfare as a whole. Semi autonomous as to its own residents but not autonomous to non residents. Jurisdictional and 'legal' laws pertaining to Courts and offenses, per se.