Are books and professional society memberships allowable expenses under US federal grants?
The page you linked to in your question directly addresses memberships for NIH:


  Dues or Membership Fees
  
  Allowable as an F&amp;A cost for organizational membership in business, professional, or technical organizations or societies.
  
  Payment of dues or membership fees for an individual’s membership in a professional or technical organization is allowable as a fringe benefit or an employee development cost, if paid according to an established organizational policy consistently applied regardless of the source of funds.


I agree with your conclusion about books for NSF grants, and their page oddly doesn't list information about memberships. I would imagine that it could arguably fall under the section related to conference fees, but that's conjecture.