The Puerto Rico Manufacturers Assn. fears that the island's apparel and shoe trades could be damaged by strengthening the Caribbean Basin Initiative and plans to testify in Washington against such a move next month. Legislation spearheaded by Rep. J. J. Pickle (D-Tex.) and Rep. Sam Gibbons (D-Fla.) would extend the Caribbean Basin Initiative, or CBI, an additional 12 years, to 2007. The measure also would allow duty-free importation of all products made from U.S. materials, including leather and apparel. The CBI was begun by the Reagan Administration to strengthen the economy of the Caribbean by lowering trade barriers.