In answering your question I am assuming that Georgia is requiring the special tavern license only for persons of Irish decent, other ethnicities not included.
Such a restriction on the part of a State would be blatantly discriminatory and therefore illegal and unconstitutional. Between the Declaration of Independence, the U.S. Constitution and the Bill or Rights, it is illegal or unconstitutional to discriminate according to race, religion, gender, age or national origin.
The Georgia law would also be unconstitutional based on the Equal Protection clause of Amendment XIV.
Also, article IV, Section 2 of the Constitution states: “The Citizens of each State shall be entitled to all Privileges and Immunities of Citizens of the several States.”
Finally, the Declaration of Independence states that “all men are created equal” and are “endowed with unalienable rights to Life, Liberty and the pursuit of Happiness”.
O’Shaughnessy would have to fight the Georgia law in Federal Court. The challenge would certainly be upheld at all levels in the Federal Court System, and therefore would never arrive for ruling in the U.S. Supreme Court.
The challenge would be upheld based upon the unconstitutionality of discrimination due to National Origin. The result would be the overthrow of the Georgia Law.