If conditions attached to Spending Clause legislation must be unambiguous, how can an agency's new interpretation of a concededly ambiguous regulation ground threatened loss of funds?

Surely someone out there knows the answer to this question that's been bugging me since the Fourth Circuit's decision in its Title IX transgender access to sex-segregated bathroom case, G.G. v. Gloucester County School Board.

Here's a Twitter version of my bleg from April 20: "Q for admin-law mavens: How square Auer deference re: Title IX bathrooms w/ Spending Cl requirement that conditions on funds be unambiguous?" 

In something closer to plain English:

Congress does not have the power to tell local school districts how to provide access to their boys' and girls' bathrooms and locker rooms. But Congress can get this power by imposing conditions on the use of federal funds provided under the Spending Clause. Congress used its Spending Clause authority to pass Title IX, which prohibits sex discrimination by entities that receive Title IX federal funds. As part of the Title IX program, the federal government promulgated a regulation that explicitly allows Title IX fund recipients to have separate bathrooms for boys and girls as long as the facilities provided one sex are comparable to those provided by the other. This regulation does not speak to the question of how to provide access to sex-segregated bathrooms for schoolchildren whose gender identity does not correspond to their biological sex. But in a new guidance document, the Department of Education and the Department of Justice have said that Title IX fund recipients must provide access to sex-segregated bathrooms consistent with each student's gender identity, regardless of whether that gender identity is consistent with a student's biological sex. 

Suppose a school that receives Title IX funds does not follow this guidance document. Can the federal government withdraw the school's Title IX funding? 

One possible answer is "yes." The federal government can impose conditions on funds, and if fund recipients don't want to comply with those conditions, they lose the funds. 

But another possible answer is "no." The federal government can't impose whatever conditions it wants on fund recipients. To be valid, a condition must be unambiguous. And the requirement to allow every student access to sex-segregated bathrooms based on the student's gender identity, regardless of what that gender identity is consistent with the student's biological sex, is not unambiguous. Violating that condition therefore cannot be the basis for withdrawing federal funds. 

What does the law say about these two answers? Any pointers are welcome.