I spelled out most of my objections to this type of thing in that first link. I'm not sure if they all apply to this situation. Andrew Stuttaford's post on "Secular Right" doesn't link to the story about the cross, so I don't have all of the info. But I just wanted to point out some things based on what is quoted:
While these battles have become all-too-familiar, there’s one showdown brewing that distinguishes itself from the rest — atheists’ demands that a cross found in the rubble following the September 11, 2001 attacks not be included in a museum that is being planned to commemorate the lives lost during the tragedy.
American Atheists (AA), a group working to advance the secular cause, has been leading the charge against the Ground Zero cross since July 2011, when the organization first filed suit against it. TheBlaze’s Meredith Jessup has explored this issue, in detail, on TheBlaze Blog, where she explained AA’s main arguments against the cross’ inclusion.
“The atheists’ suit claims that by including the cross in a museum on public property, the government is unconstitutionally endorsing a religion,” Jessup writes. “It also asserts that the mere presence of the cross would result in emotional — and possibly even physical — injuries among atheists who will feel anxious and excluded.”
Stuttaford doesn't like AA's objection to this, nor does he care for the other instances they object to. I find that odd since Stuttaford claims to be a secularist. Apparently secularism involves different things for him and I.
Again, I don't have all the info on this. So I don't know if this is really on public land or not. If it's not then put whatever you want up on the memorial. But for argument's sake I'll assume this is public land and a memorial paid for by public money.
On this issue, I just asked in his comments section, what does a cross that was found in the rubble have to do with commemorating the lives lost. What distinguishes this cross from any other object that was in the rubble with it? And why aren't any of those objects being used to commemorate the dead?
I think the obvious answer is that the cross is a religious symbol used by christians to, among many other things, commemorate their dead. I don't see any other reason why this cross would be used in the memorial. So once we all acknowledge that there is a religious motivation or purpose behind using this cross in the memorial, don't we then have to ask whether that is appropriate in regards to secularism in general and the 1st amendment specifically?