I hope we can agree that the days of "No Irish" or "No Blacks" or "No Indians" or "No..." are better off as part of history.
The idea that you can't discriminate against someone because of their race or ethnicity is broadly accepted. Courts and the (vast majority of the) American public agree that such exclusionary signs are a violation of constitutional rights.
The Second Amendment guarantees law abiding citizens the right to defend themselves, their family, and their property through the use of arms (aka guns). However, as time progressed and the Country embraced a more genteel world-view, guns have become shunned. In most states it is perfectly acceptable (and in many, encouraged) to ban guns in places of business.
That is, the business owner has the right to determine if guns will be allowed in the business. Now, one side of me is in favor of allowing business owners to make determinations for their businesses. But, they do not have the right to violate the rights of others--their personal preferences do not supersede fundamental rights.
Equally, I'm a huge proponent of State Rights and (extremely) limited Federal Government. But this isn't a State decision. A state doesn't get to pick and choose what part of the constitution it wants to uphold. I'm uncertain how this happened; how we allowed freedoms to be so easy circumvented and tucked in nice/neat boxes.
It is no more legal to place a sign on the shop window which reads, "No Guns" than a "Whites Only" sign. For reasons I can't understand we have allowed this to happen; we've looked the other way. We've allowed personal preference to erode a constitutionally protected right.
We can have the debate of if we should have the right to bear arms, but regardless of your feelings for it, we do. Given that, you can't simply say, "I'm not comfortable" with guns around. I can assume you, there are plenty in this Country who aren't comfortable with people of different colors, religions, or genders; but you can't (openly) discriminate against them. Get over it!