Yes, in many states you can. I'm not all that sure you should.
Starbucks is delightfully, refreshingly neutral on the lawful carriage of arms in their shops. They're happy to sell a cuppa joe to whoever's decent and has the price. I support them wholeheartedly in this and you oughta.
I'm not convinced your long gun needs to come along. Can it? Why, yes, in many states, it can; and you can also show up in gum boots, supershort cut-off jeans and a chain-mail top, freely expressing yourself under the good old First Amendment. But why?
4 months ago