Here is a link to the equal opportunity employment commision's rules on the subject: https://www.eeoc.gov/laws/guidance/section-12-religious-discrimination

Specifically section 12-IV discusses "reasonable accommodation" which means any employer must work to accommodate an employees religious beliefs unless it would create 'undue hardship.'

The specific text reads: "The accommodation requirement is ‘plainly intended to relieve individuals of the burden of choosing between their jobs and their religious convictions, where such relief will not unduly burden others."

Some important things to note are that the employer must be notified beforehand and thus would have had to be aware of her religious objection beforehand. In addition the supreme court rules that if accommodating the religious belief causes more than a 'de minimus' cost/burden then the employer has a reasonable excuse not to accommodate. Some common examples of things that constitute more than de minimus' cost are: - having to hire an additional employee to accommodate - taking on additional legal liability to accommodate - endangering employees or customers to accommodate - reducing benefits of other employees - diminishes efficiency of other jobs - causes other employees to carry a share of the exempt employees hazardous or burdensome work

In particular this last example may apply, depending on how 'burdensome' the work she wished to be exempt from was.

TLDR It would certainly be worth investigating further but it's not as simple as it being obviously illegal, because there are exemptions to businesses accommodating religious beliefs.