##Actually, 17 bytes

;τR9+;`$;R=Y`M@░E

Try it online!

Values are 1-indexed. This could be easily changed to 0-indexed by replacing the first R with r. But, R is what I initially typed, so that's what I'm going with.

The nonpalindromic numbers satisfy a(n) ≈ n + 10, so 2n+9 is a sufficient upper bound.

Explanation:

;τR9+;`$;R=Y`M@░E
;τ9+R;             push n, range(1,(2*n)+10)
      `$;R=Y`M@░   take values that are not palindromic
                E  take nth element

Actually, 17 bytes

;τR9+;`$;R=Y`M@░E

Try it online!

Values are 1-indexed. This could be easily changed to 0-indexed by replacing the first R with r. But, R is what I initially typed, so that's what I'm going with.

The nonpalindromic numbers satisfy a(n) ≈ n + 10, so 2n+9 is a sufficient upper bound.

Explanation:

;τR9+;`$;R=Y`M@░E
;τ9+R;             push n, range(1,(2*n)+10)
      `$;R=Y`M@░   take values that are not palindromic
                E  take nth element