It's not the source of the funds, it's that the government grant wanted to force a change of how the foundation does things, especially inclusion and outreach efforts.
1) The grant was for a specific, bounded project, but the anti-DEI terms would have applied to all activities of the Foundation, regardless of whether they were funded by the grant. (Which isn't to say that those terms would have been acceptable even for a single project, but having them apply to unrelated activities is even worse.)
2) The terms of the grant included a clawback clause - if, in the administration's eyes, the Foundation did anything to "advance or promote DEI", the grant would be rescinded, and the Foundation would be required to repay any money they had already spent. Given the size of the grant relative to the Foundation's budget, this was an unacceptable risk.
