"It is political change that the belief that all people who want to vote should be able to do so has caused".

1. "It is political change that... has caused" ...What?? "Political change" as the Subject does not make good sense here, without a Direct Object.

2. A better construction would be "The belief that people who want to vote should be able to do so has caused political change".
"The belief" is now the Subject, and "political change" is the Direct Object.