Final answer:
William Byrd, a Renaissance English composer, wrote music for both Catholic and Anglican liturgies, showcasing his talent and adaptability during a time of religious conflict in England.
Step-by-step explanation:
The Catholic composer who wrote both Catholic and Anglican music was William Byrd. Byrd was a prominent English composer of the Renaissance who managed to navigate the complex religious landscape of his time by serving both the Catholic and the newly established Anglican Church. His career flourished under the reign of Queen Elizabeth I, a period during which he composed a variety of works, including masses and motets for Catholic liturgical use as well as music for the Anglican Church, such as the Great Service and various anthems .His ability to compose music for different religious denominations is a testament to his versatility and diplomatic skill, given the religious turmoil and the shifts in power between the Catholic and Protestant factions in England. His compositions are highly regarded and continue to be performed and recorded, representing a remarkable bridging of two distinct liturgical traditions.