this is really not that complicated
the government creates a stable environment for a business to exist, provides utilities, protection via fire and police etc.. and those services are paid for by everyone. That business does not have the right to turn around and deny access to certain citizens based on their personal discrimination. The country has an interest in their citizens having equal access to a business (restaurant, store, housing) for which everyone pays the basic services which create the environment which allow that business to exist. This hasn't really been an issue in for about the last 40 years and isn't a controversy or anything that anyone (except a few kooks like Rand Paul) even talks about
BTW - Rand has since walked back his comments so apparently (if we take him at his word) doesn't even believe his own point of view anymore
Clearly this argument isn't going to go anywhere. I don't believe that any private business should be required to do business with someone that they do not want to. They have no obligation, they aren't trampling anyone's rights. Those people are free to go do business elsewhere.
The government part is irrelevent and stupid IMHO - those services that you are commenting on are paid for by everyone, including the business owners and operators, so everyone gets access to them. That does not mean that everyone is entitled to access of a privately owned and operated business, just because they pay into the same system.
No one is being denied access to any rights or systems by not being allowed to engage in commerce with a privately owned company. You seem to think that because people pay for fire, police, etc, that somehow these business are indebted to the people. They are not, as said business' also pay into the system. Those people have no more entitlement to the companies business than those business' have right to the citizens homes.