The proposed rule does not require organizations to collect/report donor SSNs. Reporting donor SSNs would be optional, and the decision of whether to do so would be left to each charitable organization.
What the proposed rule says is that, if the donor does not have a contemporary written acknowledgement of the donor's donation, and wants to use the organization’s 990 (or a new form that the IRS is considering creating) to prove that the donation was made, then that 990 (or other IRS form) must reflect both the donation and the donor’s SSN. It apparently is the IRS’ response to a tactic being used by some tax attorneys/accountants on audit, in order to get around the charitable donation documentation rules.
Most charitable organizations provide a contemporary written acknowledgement to donors, so this proposed rule should not be a major concern to them. Of course, if the proposed rule is adopted, charities should consider putting a policy in place to deal with this issue, which addresses whether and in what circumstances to disclose donor SSNs to the IRS and how to protect donor SSNs that they retain for that purpose.