If it's illegal to discriminate against those with homosexual attraction, it should be illegal against those who in their private capacity express opposition to homosexual activity on religious or moral grounds.
More than that, Title VII of the 1964 Civil Rights Act prohibits religious discrimination and has been held to require employers to make "reasonable accommodation" to employees' religious practices. It looks like Mr. Barber has a strong case here, especially because there is no Federal law prohibiting discharge of homosexual employees for their sexual orientation.