Regardless of what's even in the document, the core issue is the administration effectively attempting to punish universities who do not agree to whatever standards they dictate. Not because anything actually against any enacted state or federal law, or even standards set out for every university, but based on policies the executive can arbitrarily decide for a handful of schools. That's why you're seeing such push back.
As for the document itself, it's a bit of a mixed bag, with a lot of subtle gatchas to make it sound enticing on the surface, but more sinister the closer you look. I honestly like some of the proposed tuition changes, but there's some language regarding enrollment that I find problematic. However, since the whole thing is being given to them with the threat of a knife hanging over their head, you're going to see a lot of universities be opposed to this.
Does it? The entire Compact document is contradictory. "We don't want diversity initiatives unless they benefit the white American and conservative thought."
"We want only the best and brightest to be let in, unless they are foreign or female."
I looked for your quote "We don't want diversity initiatives unless they benefit the white American and conservative thought." but couldn't find it anywhere.
The document was carefully written to look innocuous and reasonable (unlike most Trump communications). However, a close reading indicates that it's a clever trap that gives the government a great deal more power and oversight. Combined with the known ideology of Trump's supporters, it's not hard to see that the document was not intended to be a simple, good-faith attempt at undoing some of modern academia's excesses.
I agree with many of the principles in the document, but I'm good at reading between the lines and determining the true intent of the authors.