Smh. Anyone is suspectible to Genjutsu, which is why Sasuke had been caught in Itachi's Genjutsu loop in their battle. The Byakugan doesn't grant it's user any less susceptibility than anyone else. What the Byakugan, and the other Doujutsu do grant however, is an improved insight. This however, doesn't correlate to being able to break a Genjutsu initially.
To break a Genjutsu, one must first realize one is inside of a Genjutsu. You can have any of the three Doujutsu, but if you cannot recognize reality from illusion, Byakugan, Sharingan, nor the Rinnegan are of help until REALIZATION, between true & false is accomplished.
This is the main reason why Itachi > Hyuga because his Genjutsu prowess allows him to create a fake reality perfect in unison to reality.
That being said, any Genjutsu user capable of replicating reality can successfully catch & trap a Doujutsu user.
On my phone so typos are prone.