No. The very fact that you applied for the license means you admit that there is no right to claim. Any suit must apply to the due process of the denial of priviledge. Denial of right in the case of criminal law, requires arrest and the appropriate court venue. Civil suit does not apply to acts of legislatures covering crimes.
"I'm in no position to change anything."
You're challenging the plain English contained in the 2nd Amend to the Bill of Rights.
Two points. First, different treatment provides a basis for a 14th Amendment claim whether or not you "accept" the outcome. That was what happened with certain voting requirements, and the Black Codes in the South. Second, most criminal rights issues are addressed by the 4th, 5th and 6th Amendments, though they can also result in a 14th Amendment issue. Didn't realize we were only discussing criminal issues.
You're challenging the plain English contained in the 2nd Amend to the Bill of Rights.
No, I'm saying that every right carries the responsibility of government to ensure they don't endanger the society as a whole. That requires some limitations, regardless of the language. I have pointed out numerous examples of the First Amendment which contains plain English also.