I would say there's a blend (between hating their message and hating their "style") but that it's about 75-25 split in favor of hating their message.  If they were putting out hard-hitting general Trad messages, without SVism and BoD involved, Traditional Catholics would flock to them.
In fact, we have many people on this forum (myself included) who have no problem excoriating Bergoglio and the Conciliar Modernists, even the SSPX, often calling them heretics and Modernists ... every bit as strongly as the Dimond Brothers go after people ... except that latter go after the majority of Traditional Catholics, so they don't like being on the receiving end of it.  I'm sure that Novus Ordites consider Trads in general to be schismatic, cult-like, having Pharisaical attitudes, and motivated by bitter zeal.
So it's a combination of the two, their message and their "style"/attitude, except I believe that latter would be "forgiven" and even "appreciated" if it were not for their message.
The issue might be the feeney vs Lefebvre interpretation of EENS itself for some people, but then i think those same people wouldn’t get along with you.  But Matthew (for instance, but he’s also the one who made the big comment on the thread) gets along just fine with you, as do many other people who don’t like the Dimonds
I do think the primary issue most people have with them really is schism, including schism with members of the NO who still believe all the dogmas of the RCC, and schism from all of the various trad groups who in the vast majority of cases do on principle affirm all the dogmas of the church but disagree on interpretation.  And then saying that people who disagree with their interpretation for whatever reason were formal heretics.  They don’t just disagree with Lefebvre for example, they literally say that he was a heretic and that he’s in hell.  They even said that a sede priest who “denied eens” was in hell
Making a logical argument that the Lefebvre interpretation of eens leads to Vatican ii is very different than saying that everyone who believes it is a formal heretic and will certainly go to hell etc
and I think to start doing that to other Catholics gets goofy and cult like, in other words i think Matthew is correct