The following persons shall be disqualified for office:

First, any person who shall deny the being of Almighty God.

Second, with respect to any office that is filled by election by the people, any person who is not qualified to vote in an election for that office.

Third, any person who has been adjudged guilty of treason or any other felony against this State or the United States, or any person who has been adjudged guilty of a felony in another state that also would be a felony if it had been committed in this State, or any person who has been adjudged guilty of corruption or malpractice in any office, or any person who has been removed by impeachment from any office, and who has not been restored to the rights of citizenship in the manner prescribed by law.