Please cite the federal law that supports your assertion.
Civil Rights Act of 1964
SEC. 201. (a) All persons shall be entitled to the full and equal enjoyment of the goods, services, facilities, and privileges, advantages, and accommodations of any place of public accommodation, as defined in this section, without discrimination or segregation on the ground of race, color, religion, or national origin.
(b) Each of the following establishments which serves the public is a place of public accommodation within the meaning of this title if its operations affect commerce, or if discrimination or segregation by it is supported by State action:
(1) any inn, hotel, motel, or other establishment which provides lodging to transient guests, other than an establishment located within a building which contains not more than five rooms for rent or hire and which is actually occupied by the proprietor of such establishment as his residence
(2) any restaurant, cafeteria, lunchroom, lunch counter, soda fountain, or other facility principally engaged in selling food for consumption on the premises, including, but not limited to, any such facility located on the premises of any retail establishment; or any gasoline station;
(3) any motion picture house, theater, concert hall, sports arena, stadium or other place of exhibition or entertainment; and
(4) any establishment (A)(i) which is physically located within the premises of any establishment otherwise covered by this subsection, or (ii) within the premises of which is physically located any such covered establishment, and (B) which holds itself out as serving patrons of such covered establishment.
Nothing in the above text suggests a cakeshop that is not also a restaurant, cafe, or otherwise a "facility principally engaged in selling food for consumption on the premises" would be subject to section 201 of the Civil Rights Act of 1964.