The Securities and Exchange Commission voted Wednesday to rescind rules that had required proxy advisory firms to inform companies of how they are advising shareholders to vote in corporate elections.

Revising a rule that was voted on in 2020 and only took effect 7 months ago is an unusual move for the agency, and Republicans on the commission vocally opposed it because, they argue, the change is being made not because new information has come to light, but due to a change in the partisan makeup of the commission.

The…