I spent 2 weeks in Hungary last Autumn. Photagraphed on many stations and at the lineside with absolutely no problems at all.
In Budapest Keleti is worth a visit and as mentioned above passengers wander about on the track . I arrived on a train from Miskolc and was amazed to see many people leave the train and do this.
Deli is an ugly station and not worth visiting but Kelenfold is and can be reached by tram. Kelenfold has all passenger trains westbound from both Keleti and Deli pass through and plenty of freight. In 2 hours there I saw freight trains hauled by locos from MAV, OBB, Metrans, Constantin , MRCE and Slovakian Railways.