can a manufacturer legally copy a designer fashion product without copying the original logo? meaning the product looks identical except for the logo.

It is generally accepted that fashion products are "useful articles" that are not covered by the law of copyright. Such knockoffs appear in the market all the time. As a general matter, unless the knockoffs are palmed off as originating with, or being sponsored by, the original designer, the sale of such goods has proven to be non-actionable. You should consult with your own attorney about this.