Well if it’s excised from the segment being read, someone did it for some reason. If another segment of the Declaration was read, then of course it wouldn’t be there. But it would be hard to win; if they did include it then another set would be screaming at them about using God for commercial purposes.
Really, you are concerned about anyone who would "be screaming" about quoting the Declaration of Independence? Do people really quiver uncontrollably at the thought of someone - anyone - being offended?
Should we now avoid teaching our children about the Declaration of Independence? Should we no longer recite the Pledge of Allegiance? Where do you propose it stop? And what if these omissions offend me? Is it okay to offend only certain people without concern? Is that now legitimate?
The truth is that our right originate from our Creator. They are not man-made. They are not devised by a government. They are derived from our Creator, just as the DOI points out. If that offends some, then perhaps they need offending to wake them back to reality.