US banking regulators are pursuing a plan that could limit investment managers’ sway over governance and strategy at American banks, in a move the industry cites as an “alarming” attempt to curb shareholder input.

The Federal Deposit Insurance Corporation approved a proposal on Tuesday that would require large managers of passive investment funds to meet new restrictions before they can buy and hold large stakes in publicly traded banks.

The proposal is emerging amid concern about the power of large investors on both sides of the political aisle. Republicans are worried index funds will align with progressive activists, pushing social or environmental issues. Democrats have worried about large investors bending banks to their own purposes and whether concentrated stakes can lead to antitrust concerns.