They *are* free to do so.
The government is saying if they want to get tax payer money, they need to do a better job of providing access to jobs and education for tax payers of all colors and creeds.
Discussion
The money goes to specific research labs. Those have nothing to do with new hires, students, teaching etc. If you want to put restrictions on those labs, sure, but this request a university-wise thing.
If your contention is that because the bulk of this money goes to specific areas of the university, the letter should say it’s only those labs that should adopt the specified policies (and fix the overly broad mask thing), then I can only conclude you’re not debating in good faith and we’re done here.
No, what I said is that if government wants to make sure the money is used efficiently, which seems to be your point, it should do so by restricting how the money should be used, not how the organization, students and staff should behave.