Does either 52.225-1, Buy American - Supplies, or 52.225-13, Restrictions on Certain Foreign Purchases, apply?
(This question and response pertains to the Veterans Administration.) The prescriptions for the various clauses in FAR Part 25 (Foreign Acquisitions) and to which acquisition situations they apply can be confusing. Your question focuses on the fact that it's a contract for commercial items that involves use of a contractor's linen inventory. There are various exclusions for applicability of the clause at FAR 52.225-1 (Buy American—Supplies) so I can't provide a definitive "yes" or "no" answer. You would need to follow the decision flow at FAR 25.1101(a)-(c). There are also exceptions to the Buy American statute at FAR 25.103. However, based on the information in your question I would assume the Israeli Trade Act and Trade Agreements clauses do not apply (FAR 25.1101(b)-(c)) and no exceptions at FAR 25.103 apply. This means that FAR 52.225-1 will apply if the contract is valued greater than the micro-purchase threshold. Your acquisition involves the "furnishing of supplies"; whether the supplies are "rented" or not is not relevant. The clause also applies to commercial items (except for information technology).
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Inclusion of the clause at FAR 52.225-13 is more straightforward. It should be included "...in solicitations and contracts, unless an exception applies" (ref. FAR 25.1103(a)). The exception is contained in the clause itself, and does not appear to apply in your situation.
A quick review of the supplemental guidance in VAAR Part 825 does not indicate any additional exclusions or exceptions. In summary, based on the limited information in your question it appears that both clauses would apply.