Just to be clear, the initial linked Q&A does not show that bakers in certain US states can legally refuse service on the basis of sexual orientation, is concludes that federal law does not prohibit discrimination based on sexual orientation. Colorado law does.
So in Colorado, you would be open to a discrimination lawsuit, if you specifically refuse to make cakes for weddings involving one or more minors. You can refuse to make cakes for minors (age discrimination is not forbidden), but you cannot refuse to make cakes for minors getting married. Then you would have to appeal the ruling up to the Supreme Court. The basis for your appeal would be the Free Exercise Clause: government may not prohibit you from freely exercising your religious beliefs.
As demonstrated in Masterpiece, the legal proceeding against you by the government cannot evince
"clear and impermissible hostility toward [] sincere religious beliefs". That ruling is distinct from saying "must always roll over in the face of an alleged belief". The first paragraph of the holdings
allows that "religious and philosophical objections to gay marriage are protected views and in some instances protected forms of expression", and grant's that the artist's decisions about how to use his expressive skills "has a significant First Amendment speech component and implicates [] deep and sincere religious beliefs". But there was no specific holding that the Free Exercise Clause provides an escape from anti-discrimination laws.
There is no bright line yet drawn by SCOTUS on this topic. One thing that seems clear is that the courts will take a second look at compelled speech, and especially compelled speech that forces a person to repudiate their fundamental beliefs.
Reynolds v. United States, 98 U.S. 145 (polygamy is against the law) provides a limit on the Free Exercise Clause as an absolute: "A party's religious belief cannot be accepted as a justification for his committing an overt act, made criminal by the law of the land". The court there state that
we think it may safely be said there never has been a time in any
State of the Union when polygamy has not been an offence against
society, cognizable by the civil courts and punishable with more or
less severity. In the face of all this evidence, it is impossible to
believe that the constitutional guaranty of religious freedom was
intended to prohibit legislation in respect to this most important
feature of social life. . . . Can a man excuse his practices to the
contrary because of his religious belief? To permit this would be to
make the professed doctrines of religious belief superior to the law
of the land, and in effect to permit every citizen to become a law
unto himself.
See also Davis v. Beason, 133 U.S. 333, for the same conclusion about the subordination of religious beliefs to the law of the land. However, the reasoning cited there:
It was never intended that the first Article of Amendment to the
Constitution, that "Congress shall make no law respecting the
establishment of religion or prohibiting the free exercise thereof,"
should be a protection against legislation for the punishment of acts
inimical to the peace, good order and morals of society
probably would not fly in the current court (the question would be, what does the text say?).
