The Commerce Clause grants powers to Congress, it does not limit the powers of states.
If someone uses Square to accept a payment or receive the benefit of a payment within the state, they can regulate it. If Square disagrees or believes the law is unjust, they can cease business in the state, or file a lawsuit against the state.
I don't think that's true; if you Google "dormant commerce clause", you'll see why. State laws restricting interstate commerce have to have a legitimate interest for that particular state and their interference with interstate commerce has to be outweighed by their benefit.
My point still stands that its up to the state to make the determination, not you or I. Obviously they feel that Square is doing something that they can regulate.
Not really. See Gonzales v. Raich for an exegesis of commerce clause jurisprudence. This is one of those cases where I think Justice Thomas' argument is correct, but that would require overturning Wickard v. Filburn, a landmark case. These cases aren't about banking specifically, more about the reach of the federal government.
If someone uses Square to accept a payment or receive the benefit of a payment within the state, they can regulate it. If Square disagrees or believes the law is unjust, they can cease business in the state, or file a lawsuit against the state.