I'm really just asking questions, not posing arguments, the main question being the first. At what point would the frequency turn people against mandates? >

Using the 'frog in the slowly boiling water' analogy, with some mass formation psychosis thrown in, i'd say people (meaning 70%) could be persuaded to accept almost anything.

The path we're on I'd predict QR-codes for scanning your DNA are not far away - followed not long after by 'breeding certificates' - in order to keep everyone safe it's important that only those 'genetically suited' to combating the Next Disease X are permitted to reproduce (unless you have an exemption, such as being rich and powerful).