The business has the right to establish conditions upon which you may enter its property. If a business owner chooses to prohibit weapons on its premises, that is within his/her rights. I typically interprest such business owners as having an intense desire that I transact with other business owners, and honor their wishes.
I agree. I have a concealed carry permit, and generally go about my daily business armed; at least every place that I can legally do so.
When I see a place of business that is "posted" for no firearms, I usually will try to talk to them about it. I secure my weapon in a lockbox in the trunk, go inside, and ask to speak to the manager. I politely explain why I will never do business with them. Often I will hear that it is a straight business decision: they think they will attract more business by "posting" than they will drive away.
I personally am just fine with this. It seems like a reasonable balancing of rights to me.