Early primary states have disproportionate influence on the nomination process, because they set the early narrative concerning which candidates are doing well or poorly.
For some time now, the earliest primary states (Iowa and
New Hampshire) have been unusually rural and conservative, which gives an advantage to conservative candidates.
In an attempt to reduce that advantage,
the Democratic National Committee (DNC) has approved a plan that would make South Carolina the first state to hold a Democratic primary in 2024, with New Hampshire and Nevada following three days later.
State and party officials in Iowa and New Hampshire have objected to this plan, and are fairly likely to proceed with dates that violate the DNC plan. The DNC can penalize states that ignore the DNC plan by reducing the number of delegates those states can send to the Democratic Party's nominating convention. That enforcement mechanism has no direct effect on the Republican Party's process.
To conform to the DNC plan, a few states may end up holding their Democratic and Republican primaries on separate days, but the number of states that can do that is limited by state laws (which vary from state to state) and political considerations within state legislatures and each state's party apparatus.