The public network is providing access to Coursera’s Career Academy, which includes professional certificates from companies like Microsoft and Google.
The union alleged that the agency's recent guidance barring colleges from considering race in any of their programs and policies is unconstitutional.
Neeli Bendapudi said the university will review a dozen of its commonwealth campuses to determine which will stay open and which will close.
"Religious institutions cannot discriminate on the basis of sex, even if motivated by religion," the judge wrote.