Chlorine (Cl) and bromine (Br) are rare elements when considering the whole Earth. However, being highly volatile elements, their delivery and retention processes during planetary accretion and chemical differentiation provide important clues about the formation of the Earth. Variations in Cl and Br isotopic systems (37Cl/35Cl or δ37Cl and 81Br/79Br or δ81Br) among terrestrial reservoirs could trace these processes. While the Br isotopic value of the mantle remains entirely unknown, the measurement of mantle Cl isotopic values is a controversial subject, with measured δ37Cl values ranging from -3 to 0‰ in mid-ocean-ridge basalts (MORBs) and from -2 to +3‰ in oceanic island basalts (OIBs). Here, we report newly-determined δ81Br and δ37Cl values, together with noble gas 3He/4He (R) ratios, measured in geothermal fluids from production wells of three Mexican fields: Cerro Prieto, Las Tres Vírgenes, and Los Azufres. Relationships between 3He/4He ratios and both δ37Cl and δ81Br suggest that geothermal fluid volatiles have three distinct sources: (1) a local crustal source, enriched in radiogenic 4He (R = 1.7-1.9Ra, where Ra is the atmospheric 3He/4He ratio), and halogens from brines with δ37Cl and δ81Br of +0.1 and +0.3‰ respectively; (2) the mantle wedge, with 3He/4He ratios of 6-6.5Ra, typical of arc volcanism, and δ37Cl and δ81Br of -0.4 and -1.0‰ respectively, typical (for Cl) of fluids derived from the dehydration of serpentinite in the subducting slab; and (3) a mantle source, with 3He/4He ratios of 7.7-8.2Ra, typical of MORBs, and δ37Cl and δ81Br of +0.9 and +0.7‰ respectively. These results suggest that the primitive mantle Cl isotopic composition was positive - possibly ≥+3‰, as measured in some OIBs - and inherited during the Moon forming impact. The progressive subduction of isotopically lighter halogens over the last 2-3 Ga could have progressively lowered this initial value to those currently measured in the depleted mantle beneath Mexico. It is speculated that the different isotopic values measured in mantle rocks and fluids could reflect the heterogeneous regassing of subducted halogens and the inefficient homogenization of recycled material in the MORB source, as suggested in other studies by the heterogeneous isotopic compositions of the heavier Ar and Xe of the convective mantle.