> then that implies there's must be a conspiracy acting against said majority.

Or that immigration simply isn't their most important policy, even though they support stricter measures.

Imagine you have a choice between two parties: party A wants to detonate an atomic bomb in the capital but also create well-funded animal shelters. Party B opposes the destruction of the capital city, but they want to turn all puppies in the country into kebabs. What do you vote? You don't want to eat ground puppies, do you?