I agree with the spirit of what you are saying but disagree on the letter when it comes to matters of law. When church service is on, or the church is otherwise open to the public, it is “open for business” in common parlance. However, I disagree that it “does business” in the same way that any other kind of public place does. That is because the First Amendment is clear:
Congress shall make no law respecting an establishment of religion, or prohibiting the free exercise thereof; or abridging the freedom of speech, or of the press; or the right of the people peaceably to assemble, and to petition the Government for a redress of grievances.
It’s just not equal in the eyes of the courts, the law, or in legal standing. You don’t need a business license to open a church, to my knowledge. Even if you did, that doesn’t change their tax exemption status and other exemptions and differences in operation and interfacing with other legal and zoning entities. They are not treated equally under the law as other institutions. In some ways they are legally similar to schools and other higher learning institutions in the regulations which apply to church property; firearm regulations, for instance, apply to schools and religious places of worship differently than your home, or in your car, or on the street or sidewalk.
You can’t equivocate because religious places of worship are not equal to places of business. In the eyes of many churches, the congregation is the church proper, not the building, so if you ban the gathering, you have banned the exercise of another’s religious beliefs in a real, meaningful way. That is the part which is unconstitutional, which is where we disagree on the letter of the law.