Current Utah law lets voters join a party on primary day. However, current Utah law says that effective July 1, 2013, that policy ends, and the only voters who can vote in a closed primary after July 1, 2013 will be voters who had joined that party at least a month before the primary.
But on January 28, the House Government Operations Committee passed HB 262, which keeps the current policy in place indefinitely. In other words, assuming the bill passes, the policy that lets voters register into a party on primary day will continue to exist.
Utah has four qualified parties (Constitution, Democratic, Libertarian, and Republican). Each party decides for itself which voters may vote in its primaries. Currently, only the Republican Party requires its primary voters to be members of the party, so the bill only affects Republican primaries. Thanks to Nancy Hanks for this news.