It seems to me that if Trump is violating the Emoluments Clause by profiting off of his businesses then Gorsuch is complicit by appearing at one of his businesses and lining Trump's pockets. Not to mention that it brings into question his loyalties and erodes public confidence. Therefore, Gorsuch should avoid this conflict and decline.

Canon 2: A Judge Should Avoid Impropriety and the Appearance of Impropriety in all Activities

(A) Respect for Law. A judge should respect and comply with the law and should act at all times in a manner that promotes public confidence in the integrity and impartiality of the judiciary.

(B) Outside Influence. A judge should not allow family, social, political, financial, or other relationships to influence judicial conduct or judgment. A judge should neither lend the prestige of the judicial office to advance the private interests of the judge or others nor convey or permit others to convey the impression that they are in a special position to influence the judge. A judge should not testify voluntarily as a character witness.

(C) Nondiscriminatory Membership. A judge should not hold membership in any organization that practices invidious discrimination on the basis of race, sex, religion, or national origin.