To clarify, I am not positing any visible political distinction. Heretics aren't organised enough for that. I do not think heretics deliberately identify themselves with either elder wyrm. Most heretics probably don't even know there are these two elder wyrms. I'm suggesting, rather, that there are different ideological trends among heretics. They don't all want the same thing.

Thus, for instance, the false Guillaime spoke about being "blessed with power far beyond your ken", and when defeated, said, "Blood has been repaid with blood, and for that I am content". (Both from 'The Heretic Among Us'.) The impression I got there was that heresy was both about vengeance, making Ishgard suffer because all Ishgardians are complicit in an injustice, and about gaining more personal power. By contrast, while Ysayle embraced a plan that would harm innocents, that harm was not the point. Guillaime denied that any Ishgardians were innocents; Ysayle granted that some were innocents, but felt that ending the war was worth the collateral damage.

So I think you can talk about different heretics having different goals and different methods. Some want peace and coexistence, while others want revenge and the destruction of Ishgard. There isn't a single heretic creed. I linked these different views to Nidhogg and Hraesvelgr more because those are the two visible political factions among the dragons. (I think a few elements of Ratatoskr's brood survive as well, but never mind them.) If heretics take their cues from dragons, they are likely to come from one of the two major dragon factions.

I didn't recall any transforming heretics when you battle Shiva in 2.4. Very well, I stand corrected there.

Her Echo had given her the knowledge that the Church of Ishgard was in the wrong - but it wasn't until then that she considered the fact that the dragons could ALSO be in the wrong, and that helping them to win the war might not solve things the way she thought it would.
I remember, on those quests, feeling that Ysayle had gotten her idea of what dragons are from Hraesvelgr, and Estinien had gotten his idea of what dragons are from Nidhogg. Thus to Ysayle, dragons are tragic beasts of great nobility and even greater sorrow, and to Estinien, dragons are vengeful monsters possessed of a hatred beyond mortal comprehension. Both of them are correct. (To an extent; I think the game wants you to be more sympathetic to Hraesvelgr than I found I could be. But let's not go into that.)

But yes, Ysayle was clearly ignorant of quite a lot about the true nature of the war at the start of Heavensward, and rather naive to boot. (Her objection to just killing Nidhogg springs to mind.) Ysayle had a glimpse of Hraesvelgr and a couple of Echo visions, and then she jumped to conclusions and did some quite awful things. She and the heretics who follow her do not have any moral high ground.