It does not harm a guitar to remove all the strings at once. Period.

It was built without the strings on there, the strings are removed if any work needs to be done inside the body without any harm being done. Why, therefore, would removing them to re-string do any harm? It is an old wives tale that taking them all off at the same time 'damages' a guitar.

If in doubt, check out this widely-used and highly-respected resource:-

Frank Ford's Comments on Frets.com