"and the only other entity that would see this is the IRS"

And anyone checking on the entity, such as the public. I use Guidestar.

"Tax-exempt forms that must be made public by the IRS are clearly marked “Open to Public Inspection” in the top right corner of the first page. These include Form 990, Form 990-EZ, Form 990-PF and others."

From: https://www.irsvideos.gov/CharitiesAndNonProfits/SocialSecurityNumbers/SocialSecurityNumbers

And...

",,,remember, when an organizations applies for tax-exempt status, or files an annual 990 series return, the law requires that both the IRS and the exempt organization make those forms available to the public. And the law does not permit the IRS to remove social security numbers from those forms before making them available to the public.

Don't put social security numbers on any version of a Form 990. There is no reason for your organization to include them The IRS doesn't ask for it and we don't want them. Here are the forms that should not include social security numbers: Forms 990, 990EZ, 990N-and 990PF – the annual returns for charities and private Foundations Form 990T filed by charities Form 5227- filed by split interest trusts Forms 1023 and 1024 – applications to the IRS for tax-exempt status Forms 8871 and 8872 – filed by political organizations The forms and their instructions are available at www.irs.gov under the Forms and Pubs."