Does the planet Pandora actively turn people insane?

Solution 1:

Yes and no. Pandora as a planet does not appear to actually cause insanity. However, The Vault appears to have a psychosis-inducing effect, evidenced by the Psychos and the vault symbols etched into...just about everything.

The Vault's insane-ifying effects seem apparent due to the Psychos and the Borderlands Wikia points to the Headstone Mine incident as a possible root cause though I must admit I don't recall that bit of the story in detail.

Pandora is however an extremely harsh and dangerous environment; this has indirectly led to the insanity of at least Patricia Tannis. If you listen to her ECHO logs, she's clearly suffering from Post-Traumatic Stress Disorder (PTSD), although the psychological effects are comically exaggerated compared to the actual condition.

In addition to PTSD, the harsh environment and "gold rush" of the Vault/Eridium has led to a kill-or-be-killed environment. Many of the characters, while not apparently insane, are incredibly murderous and amoral, probably due to this. In addition this brutality is often played for laughs and is simply part of Borderlands' distinctive style.

Note there are plenty of people on Pandora who are NOT insane (Moxxie, the Vault Hunters except Brick, Kreig and possibly Salvador) and there are characters who's apparent insanity is never explained in any way (Zed). You don't have to be crazy on Pandora, it just helps.

Solution 2:

In the Pre-Sequel, Handsome Jack was really nice. Had nothing really wrong with him. But he came to Pandora, and decides the best way to stabilise the planet is to kill everyone who appears insane! With the way he talks in BL2, it's clear something happened to Jack, and same goes for others on Pandora. But remember, people were the same on Elpis.

Solution 3:

The eridium gives off some form of radiation that rapidly causes psychosis. One of the tannis logs mentions a glow coming off of the rocks. Bandits and their vault worship are all over the galaxy. The Calypsos only organize them into a recognized force. The bandits always had that quasi-religious semi-cthulu cult thing going on.