Theravadins are considered to be substantialist by Tibetan Buddhists.
If that really is the case, it is sad, since it seems to indicate that Tibetan Buddhists who hold this view, live in their own separate bubble of misunderstandings. They need to break through this bubble and discover the real world.
I have read Theravadins who definitely hold what I would consider substantialist views. I have read Thervadins who do not. I find some Abhidhamma to be very substantialist in tone.
Mahāyāna bodhicitta does not exist for most Theravadins, and the narrow criteria for who can generate something resembling Mahāyāna style bodhicitta is so strict as to discourage anyone from trying (one reason, you see, why the Saddharmapundarika predicts everyone for full buddhahood as conceived by the authors of the Pundarika).
There once were schools - like the Sarvastivada and the Pudgalavada schools - that might be called substantialist (although I am not quite sure if that would be a correct description of them, either).
Yes, it is. They really do assert things really exist on some level or another -- atoms, moments, persons, etc. Early Buddhists went crazy with a proliferation of dharmas to explain everything, just as Mahayanists went crazy with cosmic narratives ala Puranas.
If those schools were denounced as substantialists by the Mahayana/Vajrayana - and subsequently called "Hinayana" - and if then afterwards a further misunderstanding led to Theravada being identified as "Hinayana", that might perhaps explain how such a bizarre view arose.
Well, in my opinion the distinction between Mahāyāna and Hināyāna really hinges on how vinaya was interpreted more than anything. Mahāyānists consistently maintain that intent is more important than the vow. That under certain circumstances a monastic could even kill a human being, lie about miraculous powers, etc. without losing his monastic vows. Mahāyānists felt that many monastics used their vows as an excuse to disengage from the world. There is element of "engaged" Buddhism in the formation of early Mahāyāna that has been overlooked. Of course, at the same time, there also trends in Mahāyāna that suggest withdrawing from the world.
Mahāyāna is not a coherent, monolithic entity either. This is perhaps the most important thing to recognize -- apart from distinct features common to all Mahāyāna schools, the development of Mahāyāna was not a rational evolution, the development of any system of thought with many contributing thinkers never is (including Theravada).
So called Modern Mahāyāna is basically a scholastic fabrication every bit as much as Modern Theravada is.
The fact is that circumstances on the ground are not so easy -- there used to be Mahāyāna Thervadins until they are were crushed in Shri Lanka. So, in general the main line of division is that all monastic orders belong to a so called "hināyāna" because their goal and intention is inferior and lower. The vows of monk are the essence of "hināyāna" because they are so restrictive. Theravadins, etc., thought it was scandalous that so called Mahāyāna bhiksus would freely handle gold, sometimes go to bars, and generally mix with the population. In some ways the monastic orders were too elite oriented and this created a vacuum where the populist Mahāyānis could easily fill. It is often easier to get your spiritual milk from the guy you drink beer with than a priest. This also explains the popularity of the siddha movement later on.
Mahāyāna was originally sub-altern movement that was bucking the monastic establishment while at the time trying to co-opt it. It also did not develop rationally, but was rationalized by later Mahāyānis once certain Mahāyāna trends were set as "establishment" and gained royal support post Nāgārjuna. Nāgārjuna's secured his place in history no so much because of what he wrote, but because of who his friends were (kings). This is the way of samsara.
Then Mahāyāna grew stale, abstract, irrelevant to needs of normal people and we have another sub-altern movement, anuttarayoga tantra (I exclude lower tantras because these were never sub-altern movements -- but from the beginning grew out of a need to parallel the replacement of brahmins in the burgeoning context of a growing Puranic culture for ritual needs of the aristocracy and commoners).
Finally, the Huns, then Hindu Kings, and finally Persian Moslems burnt, dismembered and interred Buddhism in its homeland over a period of 700 years.
We need to not forget that -- and we need to make sure our Buddhism, whatever it is, is as relevant to the beer drinker (without of course insisting that he give up his beer) as it is to a scholar.
Buddhism is a vast tree planted in the soil of India, which shot out runners in many different directions. All of our Buddhist teachings are shoots from that tree, at least in this era. There were other Buddhas, other eras. But root, trunk, branch, leaf, and flower all lead to but one result. Awakening. And that is the most important thing to recall when conversing and discussing with our fellow Buddhists.