I disagree with this:
Jail for someone, failing to do their job seems in appropriate in a free society to me. Jail is, or should be reserved for a small set of grievous acts against others. Not doing your job generally doesn’t reach this level.
Make no mistake, she’s not doing her job. The best parallel I can think of is a tank driver, or bomber pilot refusing to fire on the enemy, perhaps at a crucial time because they are opposed to violence because of their religious beliefs. You can support, or at least respect their dedication. You can’t leave them in the tanks and planes. You take them out of battle as a conscientious objector.
Normally, if you can’t or won’t do a job, you should quite. Its wrong to take the position if you won’t do the work, and that’s what going on here. In short, I think she should quite, not stay in here position but refuse to do the job. Failing that she should be removed from office however necessary.
Those who oppose her views should also be aware that putting her in jail, will almost certainly make here a marauder. Is that what they want?