Mod 1, “30-60 inventory” id 1374169792 – One half of the reason for conflict. Sets inventory size to 30 or 60, optionally adds backpack and amulet slots.
Mod 2, “Pouches” id 423855646 – The other half. Among other things optionally adds backpack slot and optionally adds amulet slot.
Mod C1, “60 Slot itembar [en] Correct (Origin)” id 903705508 – used for comparative testing sets inventory size to 30-60, doesn't add slots (but has an annoying quirk of shifting inventory position when backpack is equipped, which is not present in it's counterpart)
Mob C2, “Backpack and Amulet slots” id 277517714 – also used for comparative testing. Adds backpack and amulet slots.

The only DLC I own is RoG so that's what this was tested on.

Tested configurations and results.
2 with slots + C1 = works
2 with slots + C2 = works, but creates duplicate slots, functioning as the same slot shown twice
2 with slots + C1 + C2 = works, but creates duplicate slots, functioning as the same slot shown twice

1 with slots + C2 = works, but creates duplicate slots, functioning as the same slot shown twice

1 with slots + 2 without slots = works
1 with slots + 2 with slots = inventory disappears (but brown background does not)
1 without slots + 2 with slots = inventory disappears

In other words when pouches is enabled and set to add backpack and amulet slots and 30-60 is enabled inventory freaks out.
Neither of those mods cause such issues with other mods with similar functions.
Disabling slots on the 30-60's size doesn't help.
There's one configuration which makes them work togather, yet it's not intuitive that one way works and the other doesn't so it's at least worth mentioning in descriptions. It's also freaky that the conflict is so specific and thus IMHO worth looking into as it may be a sign that at least one (if not both) of the mod's handling of things is fundamentally flawed and may cause bigger issues or conflicts down the line.