Our traditional calendar references of AD and BC are neither ancient nor entirely sacred in the sense of a reference to the birth of Jesus. It was first proposed in 533 by the Roman abbot Dionysus Exiguus, but as a practical matter he began counting years from from what he believed to be the year of King Herod's death1, not from the year of Jesus' birth, which he realised was unknowable. Nevertheless, the pagan Roman calendar continued in use until the ninth century, when Dionysus' calendar began to be adopted widely, with its references to AD (Anno Domini) and BC (Before Christ).
Many Christian scholars continue to use the terms AD and BC in their writing, but others have adopted the more neutral CE ('Common Era' or 'Christian Era') and BCE ('Before Common Era' or 'Before Christian Era') as much in deference to Jewish and other non-Christian sensitivities as any other reason. I have never seen any request for them to do so, either from irreligious people or people of other faiths, and therefore no refutation of such requests. Most certainly, Christian scholars are not forced to use the newer terms, as evidenced by the number of Christian scholars who continue to use the older abbreviations.
If the Christians of the early Middle Ages felt that the use of a Christian calendar, with AD and BC, was of such little moment that they delayed its use for some centuries after its development by Dionysus Exiguus, then we need not be overly concerned about whether some choose to use the same calendar, but with CE and BCE.
1We now know that King Herod actually died in April 4 BC/BCE.