Every language is Countable.
If $L$ is Non-RE language, then also $L$ is Countable.
$\Sigma^*$ is countable, and Every language is subset of $\Sigma^*,$ hence, Every language is Countable.
$L_D$ is defined as:
$L_D = \{ <M> | \text{M is a TM such that} M \notin L(M) \}$
Thus, $L_D$ is the collection of Turing machines (programs) $M$ such that $M$ does not halt and accept when given itself as input.
$L_D$ is Not-RE and we can prove it using simple “proof by contradiction”, BUT $L_D$ is Countable.
$\color{red}{\text{Watch the following playlist for understanding the concept of Countability:}}$
https://youtube.com/playlist?list=PLIPZ2_p3RNHiMGiPFIOPJG_ApL43JkILI