I can't figure out the difference that makes some cuttings in water get algae all over their jar, and others from the exact same plant, cut on the same day, same water, same batch of jars, right next to each other, never get any. This happens in the sun, in the shade, in the winter, summer, spring, and fall, so confounding.

That's a tough one. Obviously, there must be some variable that is varying. I think you've covered all the bases as far as growing environment, so it probably comes down to the innoculum source, which is quite elusive. The only thing I can think of at the moment is the water source: did you fill them all from different faucets/hoses, from the same faucet/hose, or did you fill a container (like a watering can) and use that for them all?

Answers would go from:
- very likely the problem
- likely the problem
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Thank you for your response! That's kind of the thought process I've gone through and declared myself unable to figure it out. Starting to suspect fertilizer but I used to get algae back when I would have never used fertilizer water to top-off the water for plants in water.

The algae doesn't seem to cause problems for the plants, but curiosity remains.

The sun light is the main factor in algae growth. I put my jars into another container to shield them if they are exposed to sun-light. Mine are inside or on the NE balcony , so i just can pop them in brown paper bags :), with overhang they won't get wet ..or some dark plastic/pot works too. My water usually has some liquid fertilizer added: algae love that! And i add peroxide to water too to prevent algae. it works if the sunlight is blocked. Like i use double plastic container tubs from yogurt, doubled. The single ones are somewhat translucent and they get algae.
Yr plants are outside? Then even in shade you'll get enough diffused sun to cause it.

What i don't understand is how 2 identically positioned pots can differ: one with algae, one without? All of mine get algae if not shielded well from light , even in slight shade/ in back of shelf/ balcony.
Even with peroxide added ..but that is for potted plants on wicks with fertilizer added. May be that plays a role .
i do not add fertilizer when i water-propagate: i had once left a bucket with 2qts of water on the table : last ditch effort to save a cutting (no direct sun and tented too) and i had no algae 3 months later! (It had a film covering water too).
So, of course it had peroxide added , but also water was shielded from surrounding air.
Long time ago i learned on the forum that it helps to cover the top of container with saran film with poked holes when rooting begonias in water . It stabilizes the stems and prevents air-contamination and also they develop air-roots above the water fast as there is 100% humidity between the water level and film. There are always mildew /fungal spores floating in the air-soup , so it's important to screen them out, especially for begonias.
With this method i can leave cutting for water-rooting when i am away for very long times (4-8 weeks). I started doing it when i am not away too: no need to monitor; can do many more at once.
I am very long-winded here 😁; but i think that runoff water from pots (if you water on occasion from the top) can contribute to algae growth too. Or air access to water.
So when pot is tight in the water container, not watered from top and water is shielded from light there should be no algae at all (+ peroxide added, of course).
I use huge 2.5 gal water jugs filled with water for walling off my pots on the balcony (high wind, pots might topple) when on vacation in summer: no peroxide, small half inch hole on top to fill; exposed to sun for 2-3 hours…and 1 month later they are still clean, and even after 2 months ..