Second, two of the three available are still under EUA, and the one that is approved is of a new type of vaccine that became approved through a very unconventional route, which has some folks cautious. Those other vaccines you mention are well-established and have been proven over time and through clinical testing to be safe and effective. COVID vaccines have proven to be only effective at reducing reactions, but not very effective at reducing spread.
Note that a typical clinical trial lasts years[0] - phase II usually takes 2-3 years and phase III takes an additional 2-4 years. We've had these vaccines for less than one year; if this was a typical vaccine, it'd be only part-way through phase II trials.
And now it's mandated by the government; get this shot, some of which are using new technology, that has had shortened clinical trials or lose your livelihood (because, at $14k per infraction, I don't see many large companies bothering to offer testing as an alternative unless it's for the CEO or other executives; it's just too much liability for an easily-replaceable lower-wage employee).
> but the unwillingness to acknowledge precedent is bizarre
That's because your precedent isn't an exact match, and has had easy alternatives and ways to opt-out.