Station has meant a stopping-place since the 1500s. Based on that idea, the phrase railway station has been around since the 1830s and bus station since the 1950s.
Train station is even more recent and originally an Americanism and it is basically that last fact that makes people - for reasons known only to themselves - object to it.
We have perfectly happily adopted a multitude of Americanisms over the years and I can see no reasonable objection to this particular one. You go to a bus station to get on a bus, so what earthly objection can there be to going to a train station to get on a train?