Sideboard Theory:

> R/B Midrange:

Their Problem Cards:
Graveyard Trespasser - Exiles important cards.
Bloodtithe Harvester - Can -4/-4 Soulflayer off of two blood tokens if no hexproof.
Go Blank - Exiles graveyards, importantly sorcery speed.
Extinction Event - Kills any Soulflayer setup.
Liliana of the Veil - Can force us to sacrifice a Soulflayer, bypassing all our protection.
Invoke Despair - Can force us to sacrifice a Soulflayer, bypassing all our protection.

In:
4x Abrupt Decay - Hits everything besides Sheoldred.
2x Stubborn Denial - Hits all of their sweepers and edicts.

Out:
2x Thoughtseize - Forces the game into topdeck situation while also being a terrible topdeck.
2x Fauna Shaman - Easily removed and slow.
2x Gifted Aetherborn - Dies to removal and Lifelink probably isn't necessary.

> Nykthos Ramp:

Their Problem Cards:
Cavalier of Thorns - 5/6 with reach, will block and kill a non-Zetalpa Soulflayer.
Karn, the Great Creator - Access to sideboard and silver bullets game 1.
Storm the Festival - Generates a lot of advantage that is difficult to come back from.
Nykthos, Shrine to Nyx - Nykthos is manageable as long as we can keep devotion off the board and answer whatever they play.

In:
3x Assassin's Trophy - Removes a Cavalier, Nykthos, Kiora, Karn. Very versatile panic button.
3x Stubborn Denial - Karn, Kiora and Storm, only becomes a hard counter once a Soulflayer is on board though.
2x Unmoored Ego - Almost certainly naming Karn, maybe Nykthos if Karn is already on the table.
2x Thoughtseize - Hand disruption against a combo deck is always good.

Out:
4x Fatal Push - Pushing mana dorks is good, but not where the game will be won or lost, hits nothing else.
2x Fauna Shaman - Too slow in this matchup.
2x Striped Riverwinder - Hexproof is less important against a deck with low removal. Cycling is still nice though.
2x Gifted Aetherborn - Deathtouch and lifelink don't help in the combo race.

> Gruul Boat:

Their Problem Cards:
Skysovereign, Consul Flagship - Very evasive to all of our removal as it'll most likely only be a creature on their turn. Needs a Zetalpa Soulflayer to get through it.
The Akroan War - Will steal a non-hexproof Soulflayer for multiple turns.

In:
3x Assassin's Trophy - At the cost of a basic land, kills any threat, the panic button.
3x-2x Abrupt Decay - Destroys every creature in the deck, on the play 3x Decay, 1x Push, on the draw, 2-2 split.
1x Haywire Mite - Can kill vehicles in response to being crewed, The Akroan War, and is fetched by Fauna Shaman.

Out:
3x-2x Fatal Push - On the play 3x Decay, 1x Push, on the draw, 2-2 split.
2x Fauna Shaman - A little too slow and easily stomped.
2x Thoughtsieze - Unless I'm discarding an Akroan War or Skysovereign, this isn't worth it here.

> G/W Angels:

Their Problem Cards:
All the angels have flying, so our usual evasion won't be as good.
Deafening Silence - This isn't as bad as it looks as we can play a lot at instant speed, removed fairly easily by Abrupt Decay if it gets too taxing.
Shapers' Sanctuary - To slow them down enough to set up Soulflayer, we're going to need to remove their creatures, Sanctuary gaining them a card each time we do is pretty bad.

In:
4x Abrupt Decay - Removes every non-land permanent in their deck, always a good card to have in hand.

Out:
2x Striped Riverwinder - They have no removal that hits a 4BB creature, so hexproof isn't needed in the Soulflayer pile, cycling is still nice though.
2x Thoughtseize - Discarding a Collected Company is nice, but they're a pretty resilient deck.

> Lotus Combo:

Their Problem Cards:
Lotus Field - Gives them the mana to win fast.
Emergent Ultimatum - Tutors for their combo
Languish - Kills any Soulflayer setup.

In:
3x Stubborn Denial - Usually win attempts will come after resolving a Soulflayer, meaning this is a hard counter for U.
2x Unmoored Ego - Essentially wins the game choosing Lotus Field, or if they already have one out, Thespian's Stage.
2x Thoughtseize - Hand disruption in the combo matchup is always good.
1x Assassin's Trophy - Boarding in answers to Zacama, Primal Calamity or Elder Gargaroth, just in case.

Out:
4x Fatal Push - Hits nothing meaningful in the deck
2x Fauna Shaman - Slower than I'd like in this matchup.
2x Gifted Aetherborn - Deathtouch and lifelink don't help in the combo race.

> U/W Control:

Their Problem Cards:
Farewell - Exiles any Soulflayer setup.
Supreme Verdict - Kills a non-indestructible Soulflayer
Teferi, Hero of Dominaria - Can bounce a non-hexproof Soulflayer
Rest in Peace - Shuts down our entire gameplan
Baneslayer Angel - Protection from Soulflayer so can block forever, needs removal.

In:
3x Assassin's Trophy - Hits both Planeswalkers, RIP and Baneslayer Angel.
3x Stubborn Denial - Hits plansewalkers, wraths and stops RIP on curve.

Out:
4x Fatal Push - Hits next to nothing in the deck.
1x Murderous Rider - Will only hit Planeswalkers, lifelink isn't needed.
1x Tainted Indulgence - Trimmed for more specific matchup cards.

>Mono-White Humans:

Their Problem Cards:
Brutal Cathar - Exiles a non-hexproof Soulflayer. Even if we get it back, it loses the keywords.
Brave the Elements - Allows them to get through damage, blank removal and force auras to fall off.
Rest in Peace - Shuts down our entire gameplan.
Thalia, Guardian of Thraben - as a low curve deck with few lands, adding 50%+ to the cost of our spells hurts.

In:
4x Abrupt Decay - Hits almost everything in the deck.

Out:
2x Thoughtseize - Hand interaction is much less important in the aggro matchup.
2x Fauna Shaman - Too slow in the matchup.

>Abzan Greasefang:

Their Problem Cards:
Greasefang, Okiba Boss - Reanimates and crews vehicles.
Parhelion II - Cheated into play
Eldritch Evolution - Finds Greasefang.
Liliana of the Veil - Can force us to sacrifice a Soulflayer, bypassing all our protection.

In:
4x Abrupt Decay - Kills Greasefang and Liliana unconditionally.
2x Unmoored Ego - Naming Greasefang means they have a hard time crewing vehicles, should slow them down enough for us to win.

Out:
4x Fatal Push - Doesn't kill Greasefang and all other creatures are only used for their etb effects.
2x Thoughtsieze - Nothing massively dislikes being in their graveyard.

>Izzet Phoenix:

Their Problem Cards:
Thing in the Ice - Can force us to return a Soulflayer to our hand if it flips.
Disdainful Stroke - Counters our Soulflayer.

In:
3x Stubborn Denial - This matchup will be fought on the stack.

Out:
2x Thoughtseize - They have large redundancies and plenty of draw, discarding Phoenixs is essentially beneficial.
1x Fauna Shaman - A little slow, trimmed to make room for specific matchup cards.

>Five-Colour Fires:

Their Problem Cards:
Fires of Invention - The engine of the deck.
Disdainful Stroke - Counters our Soulflayer.
Rest in Peace - Shuts down our entire gameplan.
Various targeted exile effects - Need Hexproof.

In:
3x Assassin's Trophy - Kills the bigger threats if they have time to stabilise.
2x Abrupt Decay - Removes their early enchantments, notably RIP.
1x Haywire Mite - Can be searched with Fauna Shaman, hits all their important enchantments.

Out:
4x Fatal Push - Not a small creature based matchup.
2x Ledger Shredder - If they're casting two spells a turn, we're probably losing.