Why do Shaefer's and Mahaney's Theorems not imply P = NP?
Schaefer's theorem applies only to a specific type of languages, those of the form $\mathrm{SAT}(S)$ for a finite set of relations over the Boolean domain or $\mathrm{CSP}(\Gamma)$ for a finite constraint language over the Boolean domain (the two notations are equivalent; see the Wikipedia page for a description). Any other language is not covered by the theorem, and the theorem has nothing to say about it. In particular, Schaefer's theorem doesn't say anything about your language $L$.