The first political passengers on modern railroad cars were a president, a senator, and a governor that had been traveling to Washington, D.C. together on the Liberty Express in 1907.
1. Verb issues and meaning(A) The first political passengers on modern railroad cars were a president, a senator, and a governor
that had been travelingThat cannot refer to people, also past perfect progressive "had been traveling" makes no sense. They were not traveling before they became the first political passengers, it was a simultaneous occurrence that happened in 1907 so we need simple past.
(D) A president, a senator, and a governor
who were the first political passengers on modern railroad cars
to travelWe have a subject and then a relative pronoun, but only one action verb "were" which is linked to "who" so this becomes a fragment. "To travel" is part of the very long string of prepositions.
(E) A president, a senator, and a governor were the first political passengers on modern railroad cars
travelingChanges the meaning, since "traveling" is now a gerund modifying railroad cars.
2. More meaning issues(C) A president, a senator, and a governor were the first political passengers on modern railroad cars
who traveledFixes the verb issue but changes the meaning again. Even if we initially miss that "who" is referring to "modern cars," it doesn't make any sense the other way, i.e. referring to the politicians because they were NOT the first passengers ONLY on the Washington D.C. line, but they were the first political passengers OVERALL.
(B) The first political passengers on modern railroad cars were a president, a senator, and a governor,
who traveledFixes the remaining issue in C) by using the pronoun "who" to introduce a dependent clause of additional information.