Government Neutrality in Contracting Act - Directs the head of any federal agency that awards or obligates funds for any construction contract, or that awards grants, provides financial assistance, or enters into cooperative agreements for construction projects, to ensure that bid specifications, project agreements, or other controlling documents do not: (1) require or forbid a bidder, offeror, contractor, or subcontractor to enter into or adhere to agreements with a labor organization with respect to that construction project or another related construction project; or (2) otherwise discriminate against such a party because it did or did not become a signatory or otherwise adhere to such an agreement.

Allows exemptions to avert an imminent threat to public health or safety or to serve national security. Allows additional exemptions for certain projects.

Directs the Federal Acquisition Regulatory Council to amend the Federal Acquisition Regulation to implement this Act with respect to the applicable federal contracts.