Party conventions or party primary elections held by political parties certified as such by the State Election Commission under the provisions of this Title to nominate candidates for any of the offices to be filled in a general or special election shall be conducted in accordance with the provisions of this Title and in accordance with party rules not in conflict with the provisions of this Title or of the Constitution and laws of this State or of the United States.

A certified political party wishing to hold a presidential primary election may do so in accordance with the provisions of this title and party rules. However, notwithstanding any other provision of this title, the state committee of the party shall set the date and the hours that the polls will be open for the presidential primary election and the filing requirements. If a party holds a presidential primary election on a Saturday, an absentee ballot must be provided to a person who signs an affirmation stating that for religious reasons he does not wish to take part in the electoral process on a Saturday.