I think you are confusing two different concepts in your question. Gifts to governmental entities are generally deductible by individual and corporate taxpayers who itemize their deductions on their federal income tax returns. But private foundations are not ordinary taxpayers and don’t need “deductions” because they don’t pay regular income tax. 

Private foundations are required to make distributions for charitable purposes equal to 5% of their net investment assets every year. Grants to 501(c)(3) public charities are considered qualifying distributions to meet this requirement, and so are grants to governmental units for public purposes. Some private foundations, as a matter of policy, will not give to governmental units because they want to support things the government won’t do and, in their view, should do. But they could give to governmental units and have the grants count toward their required distributions if they wanted to.