However, what if you are on classic rollerskis but exclusively double poling - would you select a pole length similar to your skating pole length, stick with your classic pole length, or split the difference?
In a lot of classic marathon races (such as the Swix Ski Classics series), the top racers (men and women) are exclusively double-poling the courses. They're using slightly longer poles than they'd use if they were striding - generally, 2-5cm longer. So, instead of 150cm, maybe something like 152.5. A lot of that depends on how strong the skier is, and how comfortable they are with the longer poles. This is also the case in World Cup classic sprinting - especially on courses which are being double-poled. If you have a pole sponsor, it's pretty simple to have a pair of poles for sprinting and flat[ter] courses, where there's going to be a lot of double-pole, and a pair that is "normal" for courses where you're going to stride a lot. (That's a big "if"!)
I'd imagine the length of the pole for diagonal stride and double poling should be the same. In both cases the pole travels on exactly the same plane, parallel to the moving legs and arms, and in-line with the direction of travel (even though the arms and legs are moving in a different way)
Same plane, yes, but most people are double-poling from a higher starting position than they do in striding. (Hands are getting higher.) So maybe it's the same plane, but not the same range of motion.
In skating the pole needs to be longer because it needs to be planted further out - beyond the outer edge of the pushing ski, the ski which travels further out compared to skis in classic styles.
The other thing to consider is the relationship between cycle length and cycle frequency: How far each pole push will take you, and high your tempo is. In striding, your tempo may be [approximately] between 90-150 pole plants per minute; in double-pole and skating, 60-90. Shorter poles are easier to manage with the higher tempo, but longer poles allow you to go farther with each pole plant.
It depends on what you're looking for.
Exactly. And it depends on what your strengths are. If you have very strong arms and a core that can support starting from a high hand position, then long poles may be a good option. If you're more reliant on tempo than power, then shorter poles might make sense.