Although I love my country and use our constitution as a guide to legality/morality; it is not an absolute. The constitution was written for people living 200+ years ago, when anyone who had the desire to own a farm need only apply for a homestead. No one needed to be burdened by your needs, since your needs could be fulfilled by yourself with an amount of effort deemed reasonable at the time. All of the rights that are laid out in the constitution and implied by the declaration were fulfilled by any man (except slaves) at the time.
This is no longer the case. I can't plop down on some land and start farming it. I can't fulfill my rights to life, due to the land being taken already. The day they stopped homesteading land for free was the day that our constitutional rights became a guide instead of an absolute.
You are right in saying that happiness, economics, and social status are not guaranteed, but there must be a path guaranteed to these things. You can't give me the right to pursue life and no path with which to pursue it; the obligation is for me to follow the path and do the work to pursue my goals (The path was homesteading and the work was farming). In the issue of public accommodation, these businesses are now that path. No store is obligated to give me free things (they aren't guaranteed) but, the store must still provide a path to purchasing goods (the path is guaranteed). In a post-farming society, that is a reasonable path to our constitutional rights. Without it, show me what path there is, or should we let people die despite their willingness to work, to pay for goods, and to live in peace.
You're right in saying that no man must be forced to serve another, but this applies to slavery and indentured servitude. You chose to open a store, it wasn't forced upon you. With that choice, you decided to become a form of public accommodation, a path to life, and thus curtailed your own rights. If you don't like it, open up a different business. Rights are not absolute; in the USA, you don't have a right to open a store and then discriminate, because their rights outweigh yours. That's how it works when a man cannot be self-sufficient off the land.