A word/phrase for a day when you must be extremely cautious

Beware the ides of March is probably the best known phrase that answers to your title question. The critical reference here is the assassination / justified killing of Julius Caesar. A seer warned him that danger would befall no later than the Ides.

Is it a full moon out?

As a lunatic in good company, I'm surprised no one has submitted anything related to a full moon, a time when you can relegate your behavior to the tides and fear of lycanthropy. Many people experience insomnia as a lunar effect, and it's not uncommon when things start to go sideways to hear people exclaim, "Must be the Moon."

The lunar effect:

A correlation between specific stages of the roughly 29.5-day lunar cycle and behavior and physiological changes in living beings on Earth, including humans. In some cases the purported effect may depend on external cues, such as the amount of moonlight.

Warnings are given in the same vein. It might be confirmation bias, but weird things happen during the full moon, often coinciding with notions of triskaidekaphic events and pagan holidays like Walpurgisnacht, (only once a year on 30 April).

Must be the Moon:

"Must be a full moon" is an often heard phrase whenever something out of sorts or unexpected happens. Some even believe crime goes up during that particular phase. Scientists have done studies on the "full moon effect", and contrary to popular belief, have found no correlation between the moon’s phase and crime or other unusual behavior.

Blaming the full moon for strange behavior is a time-honored tradition. In the first century AD, the Roman philosopher Pliny suggested that the full moon caused more dew to form, which led to increased moisture in the brain, and that, he said, led to madness.

And there's a lot of music to support being cautious about the waxing and waning of the moon.

If you know think something bad might happen to you, it is ominous.

According to my horoscope, today is ominous, so I'd better watch out for something bad.

Collins:

ominous ADJECTIVE

If you describe something as ominous, you mean that it worries you because it makes you think that something unpleasant is going to happen.

The rolls of distant thunder were growing more ominous.

COBUILD Advanced English Dictionary. Copyright © HarperCollins Publishers