Charity Commission for England and Wales
The watchdog is looking into "serious concerns" about the "governance and financial management" at the Aspinall Foundation.
Twelve MPs from the "Common Sense Group" called for a Charity Commission investigation over a blog post on white privilege.
It comes after a row over a tweet which appeared to show church members canvassing for Conservative council by-election candidate Jayde Edwards.
The charity has been given an official warning.
The Charity Commission said Viva Palestina's charitable funds donated by the public were "put at risk".
The organisation folded earlier this year.
Probe will look at how it handled complaints about Brendan Cox, among others.
Charity rocked by sleazy fundraising event had given £530,000.
'Many charities may not realise how vulnerable they are to the threat.'
The government wants Baroness Stowell to chair Charity Commission