Sure, but by operating a business that is open to the public, you consent to follow certain rules. In a way, a business open to the public is quasi-public: you couldn't exclude people based on race, for example. You actually don't have a constitutional right to operate a business- a local or state government can pretty much ban any type of business they want and impose whatever (constitutional) rules they desire.
I know of no "business" exclusion to the Bill of Rights. The enumerated rights in the Bill of Rights, and the other inalienable rights which are not enumerated, may not be infringed by the federal government.
The distinction that some of what we do is designed to profit us is a distinction invented by governments and collectivists. In our Founder's day, most of their daily activity was required to generate their livelihoods. I know of no intention on their part to allow a "business" distinction with regard to rights.