Hashimoto’s thyroiditis (HT) is a chronic autoimmune thyroid disease in which natural product-derived compounds may influence both immune-mediated injury and thyroid-specific physiology. This critical narrative review integrated molecular, cellular, animal, and human evidence using a dual-axis framework: H1, covering anti-inflammatory, immunomodulatory, antioxidant, and cytoprotective effects; and H2, covering direct effects on thyroid peroxidase, sodium–iodide symporter activity, thyroglobulin, thyroid-specific gene expression, and hormone synthesis. PubMed/MEDLINE, Scopus, and Web of Science searches identified 687 records; after deduplication, 356 unique publications were screened and 79 were retained for final synthesis. Human evidence was limited to three independent HT trials evaluating curcumin, Nigella sativa, and genistein. These studies reported preliminary immunological and/or biochemical thyroid-function signals, including changes in thyroid autoantibodies, inflammatory markers, TSH, or thyroid hormones. Reductions in TPOAb or TgAb are surrogate immunological outcomes and should not be interpreted as evidence of disease modification. None of the available trials established preservation of thyroid functional reserve, prevention or delay of hypothyroidism, reduced levothyroxine requirements, or improvement in patient-important outcomes. Preclinical studies supported biological plausibility but also identified direct thyroid modulation whose clinical relevance depends on exposure and context. Natural products should currently be regarded as investigational adjuncts rather than established disease-modifying therapies.