The Supreme Court said Monday that it would hear a major religious liberties case that could grant new freedoms to businesses to discriminate against gays and lesbians — and potentially others — based on the faith of the owners.

The case involves the Christian owner of a Colorado bakery who refused to make a wedding cake for a same-sex couple.

The high-profile dispute pits the rights of religious individuals against gay rights, two issues that have been at the forefront of several recent Supreme Court decisions. Both are high priorities for Justice Anthony M. Kennedy, whose vote in this matter will probably be key.

In the past, Kennedy has been both a strong supporter of gay rights and a defender of religious liberty.