SuttaCentral
In the scheme of things (mind the pun!) this is not too important. Also consider that a redactor might have analysed this idiosyncratically, and made a slight mistake 
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Abhidhamma classification, I find tend to be like this- not encompassing the whole range of possibilities… 
Agreed. Bhante hasn’t responded, so I’ll stop being a fish gasping in the air 
and will just hop back in the water. 
If you just know ‘water’ well-enough, you know earth, wind, and fire inferentially!
Sure, but I included the space element to extend the concept of decreasing resistance, ie earth, water, wind ( air ) and space. Here earth element has the most resistance, while space element has no resistance at all. Water has some resistance, but less than earth, air has some but less than water.
Note that space is one of the six properties of a person in MN140.
I was just observing that visible form ( rūpa-āyatana ) is the sense-object for the eye, which implies that there is also invisible form, ie all the stuff we cannot see. Note that we cannot see most of the stuff our bodies are made of, but MN10 includes a contemplation of these “internal” bodily elements.
From MN10:
“In this body there is the earth element, the water element, the fire element, and the air element. It’s as if a deft butcher or butcher’s apprentice were to kill a cow and sit down at the crossroads with the meat cut into portions…And so they meditate observing an aspect of the body internally.”
Sure. I’m really going on the “rupam” classification in the three categories in the OP post - I think “rupam” here is the plural of “rupa”, so on that basis I assume it’s just about the elements of form.
Yes, but as you say:
Space or akasa isn’t rupa, but delineates when the rupa begins and ends AFAIK.
This could be mental images: 
!
By all means leave out space. So earth has more resistance than water, and water has more resistance than air. This is one way of distinguishing between the elements in the EBTs.
I can’t think of any other sensible interpretation of “resistance” in this context.
And I can’t think of any other sensible interpretation of “visible”.
Anidassana vinnana is consciousnesness which is not consciousness of anything- as per Brahmin explanations, but consciousness which is conscious of things would be aware of mental objects, including visualisations.
I don’t think this is anything to do with anidassana vinnana, since there is no mention of “vinnana” in the OP quote. Neither can I see any indication that this is about mental images.
Anidassana just means “invisible”, and the OP passage is clearly referring to a 3-fold classification of rupa ( form ).
A rainbow is a visible and (in english) a non-resistant form, which would make it not fit in the three-fold classification of the physical.
Perhaps there is confusion about “resistant” or sappaṭigha. So let’s poke away and gnaw on that.
First we look at patigha, which is (ethically) repulsion, repugnance anger or (psychologically) sensory reaction. Note that anger comes into play here. With anger, delight is also implied, as is contact and suffering.
Second, we add the a- prefix for negation, arriving at appatigha not forming an obstacle, not injuring, unobstructive. Psychologically, that would be not impinging, as in “not generating contact”. This is an important word.
The, s- prefix flips it yet again from not-impinging into sappatigha for impinging.
OK. So now we have:
For me this is actually a complete classification of everything with nothing missing.
If there are no objections, I would accept this as the answer.
Bhante @sujato, the current translation of the three-fold classification of the physical in DN33 is causing a bit of confusion (see posts above). Might we have a clarification for the existing translation and/or an alternate translation to ease our befuddlement?
After days and days of struggling with rainbows, it finally dawned on me that the struggle itself was proof that rainbows are indeed resistant. 
A rainbow is a form, a perception of impingement. A rainbow is an example of a grasping aggregate. This wasn’t apparent to me until I saw the image of a cheap embroidered rainbow badge that made me turn away and “frown at the gross misappropriation of a rainbow.”
What is resistant? Fetters and hindrances are resistant. What is the counterpart of resistance? Freedom.
With this perspective, everything visible is indeed resistant. When walking meditation today, everything I saw gave either a push or pull, no matter how subtle. And the same held for all the six sense fields. I could find nothing visible yet non-resistant. Even the sky was resistant in this tiniest of ways.
Following this perspective to the non-visible and resistant, one comes up easily with examples, such as “freedom of speech”. There is push and pull there as well.
And lastly, to the third, which is invisible and non-resistant, all I can say is MN121, emptiness.
My suggestion of impingement was “close but not quite.” I had had this abstract idea that one could escape the impingement. However, I could not escape impingement in my meditation. The visible impinged one way or the other, calling to intention. And so did the invisible also call to intention. Emptiness did not call to intention because it was empty of intention.
And with this I am now quite content with the Bhante Sujato’s translation:
A threefold classification of the physical: visible and resistant, invisible and resistant, and invisible and non-resistant.
Thank you, Bhante.
I though these were three categories of form?
Hmm. The DN33 verse doesn’t mention form.
A threefold classification of the physical:
If we say that physical and form are synonyms here, then my mind can’t fit form to non-visible and non-resistant . One could say that “emptiness” is just a form (we’re talking about it) and therefore non-visible and non-resistant, but that feels a bit like odd given that suttas do talk about formless things.
Angarika Sabbamitta had suggested “sensual, form and formless” as an understanding, and that also feels like a close fit. But it didn’t quite work for me because there are the formless conscious dimensions that one relinquishes because they are still “resistant” (see MN121 progression). The only example I could come up for non-visible and non-resistant is emptiness. Per MN121, pure emptiness causes no stress and is therefore not resistant.
Because of this clash on the third phrase, I think that physical has more of a meaning of “that which is” and not particularly form.
The 3 classifications in the op verse all include ‘rupam’ which I believe is the plural of ‘rupa’ ie form. I agree though that ‘resistance’ appears to have a psychological dimension.
I thought this was a sensory artifact ofresistance or friction?
See post #29 by Karl. It depends on the translation of sappatigha.
Interesting. Since I am reading the English, I missed the “form” part: anidassanaappaṭighaṃ rūpaṃ
Well. From MN121, emptiness is essentially defined via a progressive practice away from form (e.g., village to wilderness to earth, etc.). So, in an academic sense, emptiness is defined by its inverse, which is form. In this academic sense, form is a “mathematical set” and the concept of emptiness is also a set. But then we have the experience of emptiness…
If someone can come up with an example of an invisible non-resistant form, I will revisit my answer. For me the test of non-resistant was rainbow until I realized that rainbow is indeed a form that pushes and pulls (i.e., has psychological resistance). Emptiness doesn’t and it is the only example of non-resistance I could find. Even devas are resistant because devas represent ultimate qualities. Earth is a deva and is dealt with early in MN121.
Invisible non-resistant form = air element.
As I fell I felt the wind resist my fall and whoosh past.
But air is non-resistant compared to earth and water. The only other option is space, but that is not included in rupa.