I absolutely oppose the idea of party registration to vote in South Carolina primaries.
First, I've lived in states that did that. The voter ends up being the recipient of frequent, unwanted fundraising calls by the political party with which the voter is registered. I don't want that, and I doubt that others want that either.
Secondly, I believe that party registration will result in the election of more ideologically-extreme candidates in the primaries. There won't be any mitigating forces to prevent the extremists from having their way.