I think non-christians found spiritual comfort in the cross too so there could be a case here for the provision of spiritual comfort being non-sectarian.
Why do you think that? Be specific.
Why do you believe that "spiritual"
anything can be considered "secular" under any circumstances? "Spiritual" is virtually synonymous with "religious," particularly as the term is used to describe the
cross.
If an object is placed in a museum
because it offered spiritual comfort, then that reasoning is non-secular.
If an object has a secular purpose for being placed in a museum,
any spiritual feelings or reasoning is irrelevant, so why should they be mentioned?