My take after only recently engaging with the OP fan community: this is almost always specifically about power level for their respective favourite character. Based on how the story is written, there is some ambiguity between where the 3 main fighters in the SH's stand so this is a fight over how these characters are perceived by the general fanbase. It's silly and ridiculous, but this is perceived to be a zero-sum game by these respective fan bases. Giving an inch to any of the other characters "takes away" from their own favourite.
Sanji fans try to keep Sanji paired with Zoro, drag Zoro down to Sanji, and/or put Sanji ahead of Zoro in the extreme case. Zoro fans try to lift him up closer to Luffy (or beyond Luffy in the extreme cases) and create a distinction between Zoro and Sanji. Naturally these two view points butt heads and the result is fans of one character dunking on the other.
Luffy fans are allies of Sanji fans. Despite the former downplaying both Zoro and Sanji in comparison to Luffy in favour of characters like Law and Kid, Luffy fans share a common enemy with Sanji fans in their fight over the general fan perception in power level hierarchy. Unlike Zoro, who is more ambiguous, Sanji is very clearly not at Luffy's level by direct on-panel comparisons so Sanji fans have no plausible ground to argue for that. Both Sanji and Luffy fans are aligned in their goal of downplaying Zoro in comparison to both Luffy and Sanji.
What we have is purely a numbers game. Sanji fans are outnumbered by Zoro fans, but Luffy+Sanji fans outnumber Zoro fans. This explains the "Zoro-hater" label and annoyance of "Zoro-tards", which encompasses and originates from more than just Sanji fans. On the other hand, "Sanji-haters" are mostly just composed of Zoro fans and annoyance with "Sanji-tards" is far less common because they are less "uppity".
The resulting general perception is an average of all of these factions: "Luffy is currently far stronger than both Zoro and Sanji, who are near equals". You can see this in the reddit community, where just a year ago any mention of Zoro doing anything with Kaido or soloing a calamity, would be met with downvotes and ridicule. Foreshadowing and thematic elements still fly over the heads of many to this day, but the overall fan base is warming up to the idea of Zoro doing something significant to even Kaido.
I do think this current perception will be shaken up specifically by the end of this arc. I think Zoro fans are going to win big (at least in context of the current overall perception of Luffy>>Zoro>=Sanji). I feel like Sanji will get also get a long overdue decent wanking, especially in light of the recent chapter where Oda is making playful jabs at how Sanji feels about Jinbe. Luffy and Yonko tards are gonna have their years of head canon shattered and cry "bad writing". People who love all 3 characters (like me) will just be chilling as usual.
