Words generated by CFG whose parse tree contain even number of $X$
Add a new terminal $x$ to the alphabet, and replace $X$ with $xX$ in the right-hand side of all productions. Denote the corresponding context-free grammar by $G'$, and let $h\colon A \cup \{x\} \to A^*$ be the homomorphism erasing $x$. Then your language is $$ h(L(G') \cap A^*(xA^*xA^*)^*). $$
Since the context-free languages are xlosed under homomorphism and intersection with a regular language, it follows that your language is context-free.