To be fair, though I'm not sure if they're predicating their first argument exclusively on coercing police departments or "action" by local governmental entities in general, but is this not the way that the Obama administration basically tried to force schools to protect the rights of transgender students?
You can do it with anti-discrimination regulation in schools because Title IX is
legislation that prohibits any organization receiving federal funding from discriminating on the basis of sex.
You can't do it with sanctuary city funding because there's no legislation that allows the administration to prohibit these cities from receiving federal funding because of their policies about undocumented immigrants, and it's incredibly likely that such legislation would be unconstitutional.
Trump's argument is "we have immigration laws so you should cooperate with us or we'll cut your funding, even though you're already cooperating with us to the extent that's actually required by law."
