The question is whether U.S. courts will give effect to each provision of a treaty to which the U.S. is a party.
The answer is, it depends.
What it depends on is whether the specific provision was intended to be self-executing or not.
How is this defined? One of the Conlawprofs contributed the following, from an excerpt from a short piece by Rick Kirgis (Washington & Lee Univ. School of Law) on the ASIL (American Society of International Law) web site:
Provisions in treaties and other international agreements are given effect as law in domestic courts of the United States only if they are "self-executing" or if they have been implemented by an act (such as an act of Congress) having the effect of federal law.
Courts in this country have been reluctant to find such provisions self-executing, but on several occasions they have found them so--sometimes simply by giving direct effect to the provisions without expressly saying that they are self-executing.
There are varying formulations as to what tends to make a treaty provision self-executing or non-self-executing, but within constitutional constraints (such as the requirement that appropriations of money originate in the House of Representatives) the primary consideration is the intent--or lack thereof--that the provision become effective as judicially-enforceable domestic law without implementing legislation.
For the most part, the more specific the provision is and the more it reads like an act of Congress, the more likely it is to be treated as self-executing. A provision in an international agreement may be self-executing in U. S. law even though it would not be so in the law of the other party or parties to the agreement.
Moreover, some provisions in an agreement might be self-executing while others in the same agreement are not.
All treaties are the law of the land, but only a self-executing treaty would prevail in a domestic court over a prior, inconsistent act of Congress.
A non-self-executing treaty could not supersede a prior inconsistent act of Congress in a U. S. court.
A non-self-executing treaty nevertheless would be the supreme law of the land in the sense that--as long as the treaty is consistent with the Bill of Rights--the President could not constitutionally ignore or contravene it.
Even if a treaty or other international agreement is non-self-executing, it may have an indirect effect in U. S. courts.
The courts' practice, mentioned above, of interpreting acts of Congress as consistent with earlier international agreements applies to earlier non-self-executing agreements as well as to self-executing ones, since in either case the agreement is binding internationally and courts are slow to place the United States in breach of its international obligations.
In addition, if state or local law is inconsistent with an international agreement of the United States, the courts will not allow the law to stand. The reason, if the international agreement is a self-executing treaty, is that such a treaty has the same effect in domestic courts as an act of Congress and therefore directly supersedes any inconsistent state or local law.
If the international agreement is a non-self-executing treaty, it would not supersede inconsistent state or local law in the same way a federal statute would, but the courts nevertheless would not permit a state of the union to force the United States to breach its international obligation to other countries under the agreement.
The state or local law would be struck down as an interference with the federal government's power over foreign affairs.