It is my understanding (from reading this forum) that MS allows Dems to vote in the GOP primary if they have not voted in the Dem primary.
Here in Maryland, Ds vote in the D primaries, Rs in the R primaryies, and independents don’t get to vote in the primary.
In Ohio their is no declaring of party.
When one walks into the precinct on primary day, he asks for either a republican or a democratic ballot.
So, it is the openest of open primaries.
Watching states with caucuses, I think I prefer a caucus even to a closed primary. Only the truly interested show up.