I don't know anywhere near enough about Sanguinius to metaphorically crochet him into a little finger puppet for my primarch fics but how about a little baseless speculation about him and Fulgrim? Please note that this is all based on how I view them in the universe of my silly little stories and is in no way a claim about knowing how they are in canon / lore.
I would probably a) portray Sanguinius as a genuinely sweet adorable cinnamon roll too precious for this world and b) have Fulgrim utterly loathe him because of this.
I tend to write Fulgrim as being a pleasant and charming person who, deep down, is about 50% a deeply broken overthinking ultra-perfectionist and 50% really jealous and vindictive. Please understand that this isn't me saying he's just evil and always was because it really really isn't. It's entirely possible for someone with these traits to function perfectly well in society and not be a bad person in any meaningful sense.
One of his formative experiences as a primarch was almost losing his entire legion due to the Blight corrupted geneseed that almost wiped them out right at the start.
He had to build them up himself from nothing with the constant threat of annihilation both in the sense that "if I fuck up a war and lose however-many thousand Astartes in a terrible accident on the double-ended dildo planet I have no reserves or replacements" and also "every use of our geneseed is a gamble against the horrific mutation coming back and destroying us all over again". In that context the solution he turns to, and the only one that probably makes sense based on his prior experience on Chemos, is perfection.
Make no mistakes, ever, anywhere, because the cost of failure is incalculable, even if it means committing science-treason so you can purge all weakness from your own space dudes. It's not a desire for perfection based on arrogance, although he is of course immensely arrogant in a lot of ways, but one motivated deep down by fear.
People like to clown on Fulgrim based on Jaghatai's infamous "I hear you do strange things to your warriors 😂👌" sick burn, but to be honest, viewed from his context, what Fulgrim's doing is somewhat understandable.
That is if we assume that the Khan isn't just making a cheap insult but rather is implying he knows a lot more than would be preferable about Fabius dicking around with Astartes genetics in order to detect and eliminate carriers of the corrupted gene-seed so that the III Legion, one of the smallest of all numerically, can still survive. And then a lot of other things too because, like Fabius could believably say in one of the weirder McNeill stories, forbidden science is akin to the ancient Terran delicacy known as Pringles. Once you pop you can't stop.
With that in mind it feels like a lot of Fulgrim's post-heresy actions, not just the snake orgies but the general distance and lack of care for his sons, comes from revelling in just finally being free of that level of stress and pressure weighing down on him at all times. Even Perturabo doesn't withdraw from the Iron Warriors that much and he's a dick.
Anyway, back to pre-heresy days. He has all this going on and then in comes Sanguinius with his giant fucking angel wings who everyone loves and who turned his legion into One Direction (not really but you know... perceptions vs reality and no one in this setting actually communicates with one another since they'd probably have a lot in common regarding fears of being mutants etc)
It's the kind of thing that I think would feel like a dagger in the heart to someone like Fulgrim. Directly highlighting and literally embodying all of his fears about mutation and imperfection and yet somehow appearing to get away with it while he has to exercise constant control and do horrible things simply in order for his legion to exist.
So for that reason I think he would absolutely hate Sangy and do everything he could to undermine him.
"Oh no, brother! I've accidentally spilled this entire Big Gulp cup of bright red Tizcan wine all over your beautiful white wings, and only moments before you were due to make a speech to ten million people about how wonderful the Imperium is! Let me help you clean it up."
And then he pulls out a Looney Tunes sized bottle labelled Fabius's Finest Molt-O-Matic Guaranteed Feather Remover and starts spraying it on him.
