Doesn't the Cares Act allow 100% charitable contributions deductions for 2020?

Yes.  The 100% of AGI contribution limit applies only to gifts of cash directly to charities (not including family-funded private foundations). The 100% of AGI limit does not apply to contributions to supporting organizations. The limit also excludes gifts to donor advised funds “for the establishment of a new, or maintenance of an existing, donor advised fund.”

Thanks for this answer, which is what I thought.  But then why isn't TurboTax giving me credit for the full amount of my charitable deductions and wiping out my entire tax liability?

Yes, you can deduct charitable contributions in 2020 up to 100% of Adjusted Gross Income if you itemized you deduction. If you take the Standard deductions, the maximum allowable amount is $300.