Peroxidically crosslinking or addition-crosslinking silicone rubber composition for use in the drinking water sector, food and drink sector, medical sector and pharmaceutical sector, containing - 100 parts by weight of at least one polydiorganosiloxane conforming to the average general formula R 1 x R 2 y SiO (4-x-y)/2 in which - R 1 is a monovalent C 1 to C 10 hydrocarbyl radical which is optionally bonded to silicon via an organic divalent group and contains aliphatic carbon-carbon multiple bonds, - R 2 is an OH group or a monovalent, SiC-bonded C 1 to C 10 hydrocarbyl radical which does not contain any aliphatic carbon-carbon multiple bonds, - x is a positive number, with the proviso that an average of at least two R 1 radicals per polydiorganosiloxane chain are present, and - y is a number from 1.6 to 2.0, and in which the R 1 and R 2 radicals are each the same or different, - 1 to 100 parts by weight of at least one reinforcing filler having a BET surface area of at least 50 m 2 /g, - 0.001-5 parts by weight of at least one additive - which is selected from the list comprising alkaline earth metal silicates; natural or synthetic wollastonites with or without surface treatment; aluminosilicates and the sodium, potassium or calcium salts thereof, which are also referred to as a zeolite or molecular sieve and have pore sizes of 0.3-1.0 nm; and magnesium hydroxide, - has an average particle size of 1 to 30 μm (measured to DIN 13320), and - has a pH of 7.1 to 12.0 (measured for 5 g in water to DIN ISO 787/9), - 0.1-5 parts by weight of at least one crosslinker selected from the group comprising crosslinkers for peroxidically crosslinking silicone compositions and combination of crosslinkers for addition-crosslinking silicone compositions with a sufficient amount of at least one hydrosilylation catalyst. - 100 parts by weight of at least one polydiorganosiloxane conforming to the average general formula R 1 x R 2 y SiO (4-x-y)/2 in which - R 1 is a monovalent C 1 to C 10 hydrocarbyl radical which is optionally bonded to silicon via an organic divalent group and contains aliphatic carbon-carbon multiple bonds, - R 2 is an OH group or a monovalent, SiC-bonded C 1 to C 10 hydrocarbyl radical which does not contain any aliphatic carbon-carbon multiple bonds, - x is a positive number, with the proviso that an average of at least two R 1 radicals per polydiorganosiloxane chain are present, and - y is a number from 1.6 to 2.0, and in which the R 1 and R 2 radicals are each the same or different, - R 1 is a monovalent C 1 to C 10 hydrocarbyl radical which is optionally bonded to silicon via an organic divalent group and contains aliphatic carbon-carbon multiple bonds, - R 2 is an OH group or a monovalent, SiC-bonded C 1 to C 10 hydrocarbyl radical which does not contain any aliphatic carbon-carbon multiple bonds, - x is a positive number, with the proviso that an average of at least two R 1 radicals per polydiorganosiloxane chain are present, and - y is a number from 1.6 to 2.0, - 1 to 100 parts by weight of at least one reinforcing filler having a BET surface area of at least 50 m 2 /g, - 0.001-5 parts by weight of at least one additive - which is selected from the list comprising alkaline earth metal silicates; natural or synthetic wollastonites with or without surface treatment; aluminosilicates and the sodium, potassium or calcium salts thereof, which are also referred to as a zeolite or molecular sieve and have pore sizes of 0.3-1.0 nm; and magnesium hydroxide, - has an average particle size of 1 to 30 μm (measured to DIN 13320), and - has a pH of 7.1 to 12.0 (measured for 5 g in water to DIN ISO 787/9), - which is selected from the list comprising alkaline earth metal silicates; natural or synthetic wollastonites with or without surface treatment; aluminosilicates and the sodium, potassium or calcium salts thereof, which are also referred to as a zeolite or molecular sieve and have pore sizes of 0.3-1.0 nm; and magnesium hydroxide, - has an average particle size of 1 to 30 μm (measured to DIN 13320), and - has a pH of 7.1 to 12.0 (measured for 5 g in water to DIN ISO 787/9), - 0.1-5 parts by weight of at least one crosslinker selected from the group comprising crosslinkers for peroxidically crosslinking silicone compositions and combination of crosslinkers for addition-crosslinking silicone compositions with a sufficient amount of at least one hydrosilylation catalyst.