The upthread claims were that it does, and that this is different from the US system of a limited set of specific things it is illegal to discriminate based on. I haven't endorsed either claim, merely pointed out that the example of the wedding cake case (which was based on a law explicitly prohibiting discrimination based on sexual orientation in public accommodations) is not an example contradicting the claim that the US has laws prohibiting discrimination on specific axes rather than the kind ascribed upthread to Finland.

If you have questions about the basis for the claim about Finland, you should as the poster several posts upthread who made it.