Lorie Smith, who runs 303 Creative, argued that an adverse ruling would force religious artists to carry out work on gay weddings against their religion, according to the Associated Press.
During two hours of spirited arguments, the justices appeared to split down ideological lines with the six conservatives seeming to side with Ms Smith and her supporters’ arguments.
In one awkward moment that caused a stir on social media, Justice Samuel Alito asked whether a ruling against Ms Smith hypothetically meant that a Black Santa Claus would have to take a picture with a child dressed up in a KKK outfit.
Justice Alito also asked whether the ruling would compel a photographer to take pictures for the marital infidelity website Ashley Madison.
The three liberal justices raised concerns that a ruling supporting Ms Smith would result in businesses being able to discriminate against Black, Jewish or Muslim customers, the Associated Press reported.
Justice Sonia Sotomayor said if the court rules in Ms Smith’s favour, it would be the first time that the court had ruled that a business “could refuse to serve a customer based on race, sex, religion or sexual orientation.”
Under Colorado’s public accommodation laws, any business that offers services must provide them to all customers without the right to refuse based on sex, gender, race of sexual orientation. Most states have similar laws.
In a case that has attracted significant media attention, Ms Smith has argued that this violates her First Amendment rights.
The case is the latest case to reach the Supreme Court that has seen a collision between religious and gay rights.
Amid concerns the conservative super majority could erode gay marriage rights, Congress is expected to soon pass with bipartisan support a law that would protect same-sex and interracial marriage.
Among those opposing Ms Smith is the state of Colorado, supported by 20 other liberal-led states, the Biden administration, the American Civil Liberties Union and the NAACP Legal Defense & Educational Fund.
A coalition of 20 Republican-led states are supporting Ms Smith’s case.
A decision is expected in July.