But the other thing I hear is that learning legal research and writing is really important but that the class doesn't do the trick. What really educates law students is actually doing legal research your first summer.
Therefore legal research is our most useful 1L skill, but the class is far from the most useful. IMO
I think it may depend on the school and their reputation. If a school is known for having a good LWR program, firms in the area will likely be aware of this, which means the legal writing grade will be more important.
Also, the trend towards emphasizing writing grades is new; my LWR teacher last year spent most of his career at a major west coast firm. He mentioned last year that the hiring partner, who was a close friend, had told him they were beginning to shift their policies for screening applicants in favor of stronger LWR grades. So it may not make or break you now, but it may become more of a factor in the future.