Only basic visual genjutsu. Tsukuyomi works in a split second and would be over before one brother could break the other. Sound genjutsu (Demonic flutez frog genjutsu) affect all the present in an area só both brothers would be caught.
Only Sasuke, Madara Kaguya, and maybe Obito and Nagato are immune to genjutsu. Because of Rinnegan and Rinne Sharingan.
Although Izanami might work.
Perfect jin and some others like sakon and ukon or Jiraiya with Ma and Pa on his shoulders can get caught in genjutsu but can be snapped out with the exception of IT and Izanami. And tsukiyomi will still neg as the seconds IRL can be hours in the genjutsu.
Byakyugan and Sharingan can see through genjutsu but it doesn't mean they can't be put in as evident by Tayuya's sound genjutsu. They will only be paralyze and still be able to see things in the real world. Hyuuga are also said to be able to break out of a genjutsu with ease due to precise chakra control.
Nobody is immune to genjutsu, anybody who says otherwise simply doesn't read the manga...
Immune to visual genjutsu is a possibility but there is still sound genjutsu