Background: Hashimoto’s thyroiditis (HT) is a common autoimmune thyroid disorder characterized by elevated anti-thyroid peroxidase (A-TPO) antibodies. HT frequently coexists with other autoimmune conditions, which are marked by organ-specific and non-organ-specific autoantibodies, reflecting a deregulated immune response. However, the burden and clinical significance of these circulating autoantibodies in adult patients with HT remains unclear. Methods: A cross-sectional study was conducted at the University Hospital “R. Dulbecco” in Catanzaro, Italy, from November 2023 to May 2024, involving 200 euthyroid adults. The study population comprised 100 A-TPO-positive HT patients and 100 A-TPO-negative controls, matched for age and sex. Laboratory assessments included thyroid function tests and detection of autoantibodies [e.g., antinuclear antibodies (ANA), anti-parietal cell antibodies (APCA), and anti-neutrophil cytoplasmic antibodies (ANCA)]. Cytokine profiles were also measured using sensitive chemiluminescent multi-array technology. Results: HT patients were predominantly female (77.0%) with a median age of 56 years. Compared to controls, HT patients had higher median thyroid stimulating hormone (TSH) levels (2.215 vs. 1.705 μIU/mL, p = 0.025). Circulating autoantibodies were more prevalent in the HT group, with higher rates of APCA positivity (16.3% vs. 4.1%, p = 0.008) and atypical ANCA positivity (27.3% vs. 10.2%, p = 0.003). This suggests an increased risk for autoimmune gastritis and systemic inflammation. Additionally, HT patients with positive atypical ANCA showed elevated inflammatory cytokines, particularly interleukin-1 alpha (IL-1α), in female patients (p = 0.035). Conclusions: HT is significantly associated with a higher prevalence of circulating autoantibodies, such as APCA and atypical ANCA, which may indicate a heightened risk for autoimmune gastritis and broader autoimmune involvement. Detecting these autoantibodies in HT patients could serve as markers for more severe autoimmune dysfunction. These findings emphasize the need for proactive screening, especially in older patients and those with elevated A-TPO levels. Further research is essential to better understand the clinical implications and develop targeted management strategies for these patients.