Rights are "ordered. Let's pick 3 ones you've heard of: life, liberty, and the pursuit of happiness.

Pursuit of happiness (classically understood, ignore what you've come to believe about happiness from the media) means the pursuit or acquisition of what is truly good for you.

This 'pursuit' is, however, contingent (think: "dependent") on your ability to make choices about what you do in life (liberty; going to school, picking this or that job, living in this or that place, getting married or staying single, etc.).   

And the right to pursue various choices (liberty) of course is itself dependent on your ability to live without the threat of losing your very life.

So, "compromises" among rights are settled by the "order" of rights involved among the parties in contention ("I want a cake of my choosing from this particular baker and not that other baker" ("pursuit"); "I can't go against my conscience regarding marriage" ("liberty")).

Compromise. Get a cake from another baker.