FWIW, as an OChem professor, if I give someone the option to skip an assignment, and they do, it will not effect my opinion of them.
That said, one of the benefits of the OChem exam is that it's a standardized national exam. That means that if I give it and someone nails it, I can talk about their abilities in context relative to students taking OChem nationwide with respect to percentiles.
However, in terms of overall LOR strength, I also frequently decline to write for students I've only had in class a single semester, or at least strongly suggest they look elsewhere if they have the option. There is usually very little way for it to be a truly strong enough letter for them- it ends up being a "did well in class" letter, which doesn't share much past what the transcript does, just adds a bit of fluff on top of it.