Which disease is known for causing a reddish-purple rash and is an X-linked recessive disorder?

Fabry's disease is an X-linked recessive disorder that is characterized by the accumulation of globotriaosylceramide due to a deficiency of the enzyme alpha-galactosidase A. Patients with Fabry's disease often present with a distinctive reddish-purple rash known as angiokeratomas, which typically appears in the bathing trunk area (the lower abdomen and upper thighs) and may be accompanied by other systemic symptoms such as acroparesthesia (pain in the extremities), renal impairment, and cardiovascular issues.

This disease follows an X-linked recessive inheritance pattern, which means that it predominantly affects males who inherit the affected X chromosome from their mothers. Female carriers may still exhibit milder symptoms or be asymptomatic, but they can pass the mutated gene to their offspring.

The other diseases listed do not fit the description of having both an X-linked recessive pattern and a reddish-purple rash. Gaucher's disease and Krabbe's disease are both autosomal recessive disorders, while abetalipoproteinemia has a different genetic inheritance and clinical presentation. Thus, Fabry's disease is the clear choice when considering the specific characteristics provided in the question.