Is contextual equivalence of a language with `quote`-`eval` trivial or not?
First, this entirely depends on what you take to be your set of contexts.  If (quote []) is a context, then contextual equivalence is syntactic equivalence.

Traditionally, contexts for contextual equivalence are taken to be contexts in which "expressions", in whatever meaning that has in the language, can appear. This rules out contexts like "[]", where the context places its argument inside a string literal. These kinds of contexts were also, IIRC, ruled out by Quine when he originally described referential transparency.

From this perspective, I think (quote []) is also not a context. Instead, the contexts are the places where expression evaluation could potentially happen, such as in the body of a function or in the argument of an application. 

Potentially problematically, this means that in a Lisp program with macros (or a Racket or Scheme program) you don't know what the contexts are until you run the potentially-nonterminating macro expansion process, because you don't even know where the expressions are. Whether you think this is a problem or not is mostly a philosophical question rather than a technical one.