Well, the complaints I've seen are way stupider than that, and it's that Ignis is '''''literally''''' Noctis's mother figure, this is the only correct interpretation of their relationship, and Ignoct shippers are evil because they're taking something sweet and pure and beautiful and perverting it into something "toxic" by promoting mother-son incest. There's also the "problematic age gap" argument that's oh so popular with Western fandoms these days, occasionally. Fortunately since almost everyone is 18+ there's no screeching about pedophilia except at the poor sods still shipping Noctis/Iris.
As for the people responsible, it's not exclusive to Promptis shippers. Sometimes it's Noctis/Luna fans, especially the ones who multiship Promptis, because for whatever reason similar patterns of crazy and character stanning tend to crop up in fans of both ships, even when they don't like each other. Sometimes it's Gladnis fans, who also believe that as the stand-in father figure Gladio is entitled to Ignis's love (see: Shallura shippers, who are almost identical except they're legitimately insane in that special Voltron fandom way). Of course that's not to suggest Ignoct doesn't have its own shitty fans, far from it, but in my experience their brands of toxicity usually manifest as straightforward, insufferable elitism and condescension towards other ships (a problem shared with certain Noctis/Luna fans), as opposed to relying on faux-SJ tactics to portray ship rivals as criminals.
Basically, antis are crazy, and anyone can come up with an excuse to say why a pairing they don't like is problematic because it's all rooted in meaningless ship was anyway.