You say that Karkat is easily manipulated but couldn't Sollux see when Karkat is manipulated and just tell him he's manipulated? I mean. I guess he'd be pretty angry that someone tries (and success, goddammit) to manipulate Karkat?
You also need to take into account that Sollux himself is being manipulated by those around him - he may not be as gullible as Karkat, the manipulation here is deep and complex compared to the more simplistic stuff you likely have in mind.
If someone tries to convince Karkat of something in the more simplistic way of manipulation, then yeah Sollux will catch on and step in, but in the bigger picture he can’t see through manipulation he, himself, has been subject to since the day he was born. Most of which Feferi takes advantage of, simply because she was also raised in the same environment, just on the opposite side of it.