@Eventua I don't think The Batter would be immune to telepathy. After all it's not like he doesn't have thoughts. However I believe his thoughts are so twisted, so eldritch in nature that anyone trying to read his mind wouldn't be able to really comprehend them. And if they did perchance understand what they saw they'd likely just go insane/lose a great deal of sanity from the horrifying glimpse they got into The Batter's mind.
He would likely be immune to abilities like Mind Control or attacks directed at warping his perception of things. The Batter will likely
always see the world he is in as needing to be purified and will always seek to purify things. No external force of will of any kind, however great, is likely to be able to change that given what we saw in OFF.
That said The Batter is still vulnerable to offensive and certain status dealing PSI attacks.
It's funny you brought that up because I honestly considered The Batter's resistance/immunity to certain psionic powers.
The are various ailments, afflictions, status effects, and such that Player Characters can get depending on their actions and the situations/enemies they are involved with. However I try to take every character into consideration and regardless of their sheet work to understand what might and might not effect them as much.